<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2025 Workiva-->
<!--r:3bca9667-6cbb-47cc-90f1-211e7d924d36,g:ec374a13-3cda-4913-b87e-25c8f28e839b-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/all" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#all"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#hypercube-dimension"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-default"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-domain"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/domain-member" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#domain-member"/>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/CONDENSEDCONSOLIDATEDBALANCESHEETSParenthetical" xlink:type="simple" xlink:href="kg-20250930.xsd#CONDENSEDCONSOLIDATEDBALANCESHEETSParenthetical"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/CONDENSEDCONSOLIDATEDBALANCESHEETSParenthetical" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable_bd11e407-fb96-4dba-a818-c1b48c8461e4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_StatementTable_bd11e407-fb96-4dba-a818-c1b48c8461e4" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_a4b0c109-b058-4761-838f-c7a1fbd0605f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_StatementTable_bd11e407-fb96-4dba-a818-c1b48c8461e4" xlink:to="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_a4b0c109-b058-4761-838f-c7a1fbd0605f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_a4b0c109-b058-4761-838f-c7a1fbd0605f_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_a4b0c109-b058-4761-838f-c7a1fbd0605f" xlink:to="loc_us-gaap_RelatedPartyDomain_a4b0c109-b058-4761-838f-c7a1fbd0605f_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_a41502f5-a2a1-4b91-b837-e2065aed789b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_a4b0c109-b058-4761-838f-c7a1fbd0605f" xlink:to="loc_us-gaap_RelatedPartyDomain_a41502f5-a2a1-4b91-b837-e2065aed789b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AffiliatedEntityMember_6de33829-ee2f-477e-aad4-fa0f59512ca5" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_AffiliatedEntityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyDomain_a41502f5-a2a1-4b91-b837-e2065aed789b" xlink:to="loc_srt_AffiliatedEntityMember_6de33829-ee2f-477e-aad4-fa0f59512ca5" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_b489178b-dc61-4938-b503-60f726803cb9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_b489178b-dc61-4938-b503-60f726803cb9" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiCost_fcf8f711-49a6-4583-9cd2-13ab6ea782a9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_EquitySecuritiesFvNiCost_fcf8f711-49a6-4583-9cd2-13ab6ea782a9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAtCarryingValue_6a1338ba-4a41-4a9e-8dd9-cdc0d5b2f675" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsReceivableAtCarryingValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_PremiumsReceivableAtCarryingValue_6a1338ba-4a41-4a9e-8dd9-cdc0d5b2f675" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_6a608f66-ab4a-4c4b-bb91-0bf62fa3d994" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_6a608f66-ab4a-4c4b-bb91-0bf62fa3d994" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff_a2d708d6-7a51-4628-8438-920331595b34" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff_a2d708d6-7a51-4628-8438-920331595b34" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetIncludingGoodwill_9c8be240-e715-4f69-b357-0c8811c99b79" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetIncludingGoodwill"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_IntangibleAssetsNetIncludingGoodwill_9c8be240-e715-4f69-b357-0c8811c99b79" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_5183fca3-e0df-4f35-b655-3f0d8113b126" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_5183fca3-e0df-4f35-b655-3f0d8113b126" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnearnedPremiums_be82c9ec-11a2-412d-8c2d-8fb88be672ae" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnearnedPremiums"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_UnearnedPremiums_be82c9ec-11a2-412d-8c2d-8fb88be672ae" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities_d437de0e-30aa-4f5e-8bc2-b8ff66ffd134" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities_d437de0e-30aa-4f5e-8bc2-b8ff66ffd134" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare_7fb1ead6-8a6d-40af-bff5-71167636956d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_CommonStockParOrStatedValuePerShare_7fb1ead6-8a6d-40af-bff5-71167636956d" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued_be21fca9-4198-4f52-90a2-db7a11ad8eda" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_CommonStockSharesIssued_be21fca9-4198-4f52-90a2-db7a11ad8eda" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding_3b7dd49b-d64e-496d-b900-cf828bd6c5b4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_CommonStockSharesOutstanding_3b7dd49b-d64e-496d-b900-cf828bd6c5b4" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares_b597ce55-4c61-40cf-bbbe-d90bfaa250ad" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_a22369ce-bc81-4292-a091-17c69973f737" xlink:to="loc_us-gaap_TreasuryStockCommonShares_b597ce55-4c61-40cf-bbbe-d90bfaa250ad" xlink:type="arc" order="12"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/CONDENSEDCONSOLIDATEDSTATEMENTSOFCHANGESINSHAREHOLDERSEQUITYUnaudited" xlink:type="simple" xlink:href="kg-20250930.xsd#CONDENSEDCONSOLIDATEDSTATEMENTSOFCHANGESINSHAREHOLDERSEQUITYUnaudited"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/CONDENSEDCONSOLIDATEDSTATEMENTSOFCHANGESINSHAREHOLDERSEQUITYUnaudited" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems_64cf8285-272d-4c5e-8bb1-ea5eb290bb70" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable_35c84011-7f77-4b47-8916-eaacb661b48e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_StatementLineItems_64cf8285-272d-4c5e-8bb1-ea5eb290bb70" xlink:to="loc_us-gaap_StatementTable_35c84011-7f77-4b47-8916-eaacb661b48e" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_5a2d298d-a6a1-4fb8-99b5-91ef93f34efe" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_StatementTable_35c84011-7f77-4b47-8916-eaacb661b48e" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_5a2d298d-a6a1-4fb8-99b5-91ef93f34efe" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_5a2d298d-a6a1-4fb8-99b5-91ef93f34efe_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_5a2d298d-a6a1-4fb8-99b5-91ef93f34efe" xlink:to="loc_us-gaap_EquityComponentDomain_5a2d298d-a6a1-4fb8-99b5-91ef93f34efe_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_21232263-6b55-44af-8f4e-c271e65a0bb7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_5a2d298d-a6a1-4fb8-99b5-91ef93f34efe" xlink:to="loc_us-gaap_EquityComponentDomain_21232263-6b55-44af-8f4e-c271e65a0bb7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_37183180-8c8b-4d7e-8008-62ec64cb7ff6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_21232263-6b55-44af-8f4e-c271e65a0bb7" xlink:to="loc_us-gaap_CommonStockMember_37183180-8c8b-4d7e-8008-62ec64cb7ff6" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember_aa1c7fb1-b64f-4cde-8b4b-e29875d4a4c3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_21232263-6b55-44af-8f4e-c271e65a0bb7" xlink:to="loc_us-gaap_AdditionalPaidInCapitalMember_aa1c7fb1-b64f-4cde-8b4b-e29875d4a4c3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember_b5b66b70-6d7c-4465-8e99-2dabb5d63c1f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_21232263-6b55-44af-8f4e-c271e65a0bb7" xlink:to="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember_b5b66b70-6d7c-4465-8e99-2dabb5d63c1f" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember_c0f7675c-551d-40a2-8c4e-88d09e19dc00" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_21232263-6b55-44af-8f4e-c271e65a0bb7" xlink:to="loc_us-gaap_RetainedEarningsMember_c0f7675c-551d-40a2-8c4e-88d09e19dc00" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember_317f7480-735c-4624-bd3f-8e807e7140ee" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_21232263-6b55-44af-8f4e-c271e65a0bb7" xlink:to="loc_us-gaap_TreasuryStockCommonMember_317f7480-735c-4624-bd3f-8e807e7140ee" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_64cf8285-272d-4c5e-8bb1-ea5eb290bb70" xlink:to="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_99a05f8a-d0e9-46c1-a87f-307a33bcd3a9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:to="loc_us-gaap_StockholdersEquity_99a05f8a-d0e9-46c1-a87f-307a33bcd3a9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions_5cf7e255-9b17-4a77-be60-23dfae66d41a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueAcquisitions"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:to="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions_5cf7e255-9b17-4a77-be60-23dfae66d41a" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_0ad303fe-5e36-473d-91f6-067f8ca045bb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:to="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_0ad303fe-5e36-473d-91f6-067f8ca045bb" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent_7f32f8c1-e2ce-49d1-9c73-862fa0b0c6e7" xlink:href="kg-20250930.xsd#kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:to="loc_kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent_7f32f8c1-e2ce-49d1-9c73-862fa0b0c6e7" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_a24cce6e-8f9a-40bc-aeb7-91465c9d4fa8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_a24cce6e-8f9a-40bc-aeb7-91465c9d4fa8" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss_0c8a9243-adbf-4574-96fa-bfa55803d742" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:to="loc_us-gaap_NetIncomeLoss_0c8a9243-adbf-4574-96fa-bfa55803d742" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash_e33a918c-a330-42f7-8713-d48fba80db36" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:to="loc_us-gaap_DividendsCommonStockCash_e33a918c-a330-42f7-8713-d48fba80db36" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_TreasuryStockSharesIssuedToSubsidiary_01f37741-9c81-43c1-bcd7-efdf05db6197" xlink:href="kg-20250930.xsd#kg_TreasuryStockSharesIssuedToSubsidiary"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_2da0e634-b3ea-4cee-a530-fd156e0b06b7" xlink:to="loc_kg_TreasuryStockSharesIssuedToSubsidiary_01f37741-9c81-43c1-bcd7-efdf05db6197" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_3397049e-8a74-47ba-a01c-223841fbe50c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/BasisofPresentationDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#BasisofPresentationDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/BasisofPresentationDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_652bf7ca-afcb-4df3-91c3-9be792b67b7e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_652bf7ca-afcb-4df3-91c3-9be792b67b7e" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis_af73e9f6-7030-407c-9390-f658bb4707bb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_652bf7ca-afcb-4df3-91c3-9be792b67b7e" xlink:to="loc_us-gaap_RelatedPartyTransactionAxis_af73e9f6-7030-407c-9390-f658bb4707bb" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain_af73e9f6-7030-407c-9390-f658bb4707bb_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis_af73e9f6-7030-407c-9390-f658bb4707bb" xlink:to="loc_us-gaap_RelatedPartyTransactionDomain_af73e9f6-7030-407c-9390-f658bb4707bb_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain_19e6dbd4-042e-4d26-acf2-14de8bf60b42" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis_af73e9f6-7030-407c-9390-f658bb4707bb" xlink:to="loc_us-gaap_RelatedPartyTransactionDomain_19e6dbd4-042e-4d26-acf2-14de8bf60b42" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelIntermediateLedbetterHoldingsMember_ebf293bb-b7dd-40db-89ea-80a90e12ec40" xlink:href="kg-20250930.xsd#kg_KestrelIntermediateLedbetterHoldingsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_19e6dbd4-042e-4d26-acf2-14de8bf60b42" xlink:to="loc_kg_KestrelIntermediateLedbetterHoldingsMember_ebf293bb-b7dd-40db-89ea-80a90e12ec40" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember_c2b6fe73-7b79-4f3e-9487-2f14af0667f9" xlink:href="kg-20250930.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_19e6dbd4-042e-4d26-acf2-14de8bf60b42" xlink:to="loc_kg_AmtrustFinancialServicesIncMember_c2b6fe73-7b79-4f3e-9487-2f14af0667f9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_0d045193-6150-4d46-8cda-8a56df49222a" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_652bf7ca-afcb-4df3-91c3-9be792b67b7e" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_0d045193-6150-4d46-8cda-8a56df49222a" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_0d045193-6150-4d46-8cda-8a56df49222a_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_0d045193-6150-4d46-8cda-8a56df49222a" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_0d045193-6150-4d46-8cda-8a56df49222a_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_f050dc74-1291-435e-bc91-7337d96265d8" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_0d045193-6150-4d46-8cda-8a56df49222a" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_f050dc74-1291-435e-bc91-7337d96265d8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MaidenHoldingsLtd.Member_b7ab0bce-4d7a-4c3b-bb31-a0802c90fb95" xlink:href="kg-20250930.xsd#kg_MaidenHoldingsLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_f050dc74-1291-435e-bc91-7337d96265d8" xlink:to="loc_kg_MaidenHoldingsLtd.Member_b7ab0bce-4d7a-4c3b-bb31-a0802c90fb95" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_b82bc3df-fb4b-44ca-89b7-52af1031cf71" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_f050dc74-1291-435e-bc91-7337d96265d8" xlink:to="loc_kg_KestrelGroupLtd.Member_b82bc3df-fb4b-44ca-89b7-52af1031cf71" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis_81521cbf-4915-4065-be0a-866b21589d6c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_652bf7ca-afcb-4df3-91c3-9be792b67b7e" xlink:to="loc_dei_LegalEntityAxis_81521cbf-4915-4065-be0a-866b21589d6c" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_81521cbf-4915-4065-be0a-866b21589d6c_default" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_dei_LegalEntityAxis_81521cbf-4915-4065-be0a-866b21589d6c" xlink:to="loc_dei_EntityDomain_81521cbf-4915-4065-be0a-866b21589d6c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_f8d30588-0c1c-451c-8047-4ffe03cee7e8" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_dei_LegalEntityAxis_81521cbf-4915-4065-be0a-866b21589d6c" xlink:to="loc_dei_EntityDomain_f8d30588-0c1c-451c-8047-4ffe03cee7e8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MaidenReinsuranceMember_fcf4ca4f-a206-4067-ba19-96e24f5ca51d" xlink:href="kg-20250930.xsd#kg_MaidenReinsuranceMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_f8d30588-0c1c-451c-8047-4ffe03cee7e8" xlink:to="loc_kg_MaidenReinsuranceMember_fcf4ca4f-a206-4067-ba19-96e24f5ca51d" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_c231875b-0a14-4c3a-ba2a-87827d096df7" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_f8d30588-0c1c-451c-8047-4ffe03cee7e8" xlink:to="loc_kg_KestrelGroupLtd.Member_c231875b-0a14-4c3a-ba2a-87827d096df7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis_3f978212-fb0e-4f79-8cdc-12d50c01e1fe" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_652bf7ca-afcb-4df3-91c3-9be792b67b7e" xlink:to="loc_us-gaap_BusinessAcquisitionAxis_3f978212-fb0e-4f79-8cdc-12d50c01e1fe" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_3f978212-fb0e-4f79-8cdc-12d50c01e1fe_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_3f978212-fb0e-4f79-8cdc-12d50c01e1fe" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_3f978212-fb0e-4f79-8cdc-12d50c01e1fe_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_e9fd51b2-58b5-4cf3-b28a-f920d4a75279" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_3f978212-fb0e-4f79-8cdc-12d50c01e1fe" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_e9fd51b2-58b5-4cf3-b28a-f920d4a75279" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_51c971a0-00b9-4fad-9136-0e82249aad9e" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain_e9fd51b2-58b5-4cf3-b28a-f920d4a75279" xlink:to="loc_kg_KestrelGroupLtd.Member_51c971a0-00b9-4fad-9136-0e82249aad9e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_55fcdba7-0d4e-415b-abc6-303b8858e8b6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_652bf7ca-afcb-4df3-91c3-9be792b67b7e" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_55fcdba7-0d4e-415b-abc6-303b8858e8b6" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_55fcdba7-0d4e-415b-abc6-303b8858e8b6_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_55fcdba7-0d4e-415b-abc6-303b8858e8b6" xlink:to="loc_us-gaap_EquityComponentDomain_55fcdba7-0d4e-415b-abc6-303b8858e8b6_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_d87c18ef-1c66-401e-96a8-24aa116bc515" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_55fcdba7-0d4e-415b-abc6-303b8858e8b6" xlink:to="loc_us-gaap_EquityComponentDomain_d87c18ef-1c66-401e-96a8-24aa116bc515" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_95d5c880-7976-442b-a42d-f527675a624c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_d87c18ef-1c66-401e-96a8-24aa116bc515" xlink:to="loc_us-gaap_CommonStockMember_95d5c880-7976-442b-a42d-f527675a624c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis_69261823-0d1d-45ba-91a4-23813a37edcb" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_652bf7ca-afcb-4df3-91c3-9be792b67b7e" xlink:to="loc_srt_ConsolidatedEntitiesAxis_69261823-0d1d-45ba-91a4-23813a37edcb" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_69261823-0d1d-45ba-91a4-23813a37edcb_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidatedEntitiesAxis_69261823-0d1d-45ba-91a4-23813a37edcb" xlink:to="loc_srt_ConsolidatedEntitiesDomain_69261823-0d1d-45ba-91a4-23813a37edcb_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_e6528250-8821-4cd4-bbd9-31b36a706d02" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidatedEntitiesAxis_69261823-0d1d-45ba-91a4-23813a37edcb" xlink:to="loc_srt_ConsolidatedEntitiesDomain_e6528250-8821-4cd4-bbd9-31b36a706d02" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GenesisLegacySolutionsMember_902a412c-5255-4595-a1c3-d1bb64331eab" xlink:href="kg-20250930.xsd#kg_GenesisLegacySolutionsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidatedEntitiesDomain_e6528250-8821-4cd4-bbd9-31b36a706d02" xlink:to="loc_kg_GenesisLegacySolutionsMember_902a412c-5255-4595-a1c3-d1bb64331eab" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskAxis_398fc6ea-237c-4534-9723-f77d5cf3d309" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_652bf7ca-afcb-4df3-91c3-9be792b67b7e" xlink:to="loc_us-gaap_CededCreditRiskAxis_398fc6ea-237c-4534-9723-f77d5cf3d309" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain_398fc6ea-237c-4534-9723-f77d5cf3d309_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_CededCreditRiskAxis_398fc6ea-237c-4534-9723-f77d5cf3d309" xlink:to="loc_us-gaap_CededCreditRiskReinsurerDomain_398fc6ea-237c-4534-9723-f77d5cf3d309_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain_bae79956-1121-49d8-9ebf-053f893d69d2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_CededCreditRiskAxis_398fc6ea-237c-4534-9723-f77d5cf3d309" xlink:to="loc_us-gaap_CededCreditRiskReinsurerDomain_bae79956-1121-49d8-9ebf-053f893d69d2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_HistoricReinsuranceMember_7b9a6f7b-df36-43f3-b044-e8d65bb96a08" xlink:href="kg-20250930.xsd#kg_HistoricReinsuranceMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain_bae79956-1121-49d8-9ebf-053f893d69d2" xlink:to="loc_kg_HistoricReinsuranceMember_7b9a6f7b-df36-43f3-b044-e8d65bb96a08" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage_e38f8ed9-b12e-467d-a9e0-09e65fe5fd4e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage_e38f8ed9-b12e-467d-a9e0-09e65fe5fd4e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockShareholderVotingPowerPercentage_fee61025-a7fb-41e2-8c37-3446fa54681b" xlink:href="kg-20250930.xsd#kg_CommonStockShareholderVotingPowerPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_CommonStockShareholderVotingPowerPercentage_fee61025-a7fb-41e2-8c37-3446fa54681b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare_17bab91e-c1a1-4121-8ad8-abf993fce07d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_us-gaap_CommonStockParOrStatedValuePerShare_17bab91e-c1a1-4121-8ad8-abf993fce07d" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationStockConversionRatio_0330eca9-3d7f-48ac-998a-2219ef0f977f" xlink:href="kg-20250930.xsd#kg_BusinessCombinationStockConversionRatio"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_BusinessCombinationStockConversionRatio_0330eca9-3d7f-48ac-998a-2219ef0f977f" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross_de500a71-d9d2-4636-ae1d-832a5fae8d78" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_us-gaap_PaymentsToAcquireBusinessesGross_de500a71-d9d2-4636-ae1d-832a5fae8d78" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_f49bebc7-426d-4310-9040-415df938d1fb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_f49bebc7-426d-4310-9040-415df938d1fb" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiability_ad4fdadb-f4e9-4330-a021-178182c859fe" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_us-gaap_BusinessCombinationContingentConsiderationLiability_ad4fdadb-f4e9-4330-a021-178182c859fe" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_4ecf785e-e48c-47c9-992f-63fc13b6f25d" xlink:href="kg-20250930.xsd#kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_4ecf785e-e48c-47c9-992f-63fc13b6f25d" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfDirectors_7588e36c-21b9-426e-8a49-2e1b35ad849b" xlink:href="kg-20250930.xsd#kg_NumberOfDirectors"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_NumberOfDirectors_7588e36c-21b9-426e-8a49-2e1b35ad849b" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfDirectorsSelectedByAffiliate_13615732-5503-414f-8755-a950ce1a86a6" xlink:href="kg-20250930.xsd#kg_NumberOfDirectorsSelectedByAffiliate"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_NumberOfDirectorsSelectedByAffiliate_13615732-5503-414f-8755-a950ce1a86a6" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfIndependentDirectors_6471f01a-df7d-4556-85ee-40cdbeff16a4" xlink:href="kg-20250930.xsd#kg_NumberOfIndependentDirectors"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_NumberOfIndependentDirectors_6471f01a-df7d-4556-85ee-40cdbeff16a4" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_01734681-dacc-4b4a-a343-ae7dc83a9889" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_01734681-dacc-4b4a-a343-ae7dc83a9889" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfInsuranceCarriers_bd6b8b06-75d9-4ee1-af37-54a91ea7ab78" xlink:href="kg-20250930.xsd#kg_NumberOfInsuranceCarriers"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_NumberOfInsuranceCarriers_bd6b8b06-75d9-4ee1-af37-54a91ea7ab78" xlink:type="arc" order="12"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessAcquisitionOptionTerm_44144e71-3835-41b9-9f51-cae9358d0894" xlink:href="kg-20250930.xsd#kg_BusinessAcquisitionOptionTerm"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_BusinessAcquisitionOptionTerm_44144e71-3835-41b9-9f51-cae9358d0894" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceAgreementOpen_de828bf0-61de-41a0-84f0-c831fc6ca8ac" xlink:href="kg-20250930.xsd#kg_ReinsuranceAgreementOpen"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_ReinsuranceAgreementOpen_de828bf0-61de-41a0-84f0-c831fc6ca8ac" xlink:type="arc" order="14"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceAgreementCompletingRunOff_f1e72e87-bad0-4456-9ed4-9ea98165d457" xlink:href="kg-20250930.xsd#kg_ReinsuranceAgreementCompletingRunOff"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_e06dc268-01ab-44e2-b824-8a011ced952f" xlink:to="loc_kg_ReinsuranceAgreementCompletingRunOff_f1e72e87-bad0-4456-9ed4-9ea98165d457" xlink:type="arc" order="15"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/SignificantAccountingPoliciesDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#SignificantAccountingPoliciesDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/SignificantAccountingPoliciesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_c29bbf11-f8a3-440d-84e1-cd45e8a304f0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_58410d05-09c5-421d-b44c-7af1f9d79f0c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_c29bbf11-f8a3-440d-84e1-cd45e8a304f0" xlink:to="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_58410d05-09c5-421d-b44c-7af1f9d79f0c" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_6ef0316f-219a-4d57-8c2f-8efe2c7567cc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_58410d05-09c5-421d-b44c-7af1f9d79f0c" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_6ef0316f-219a-4d57-8c2f-8efe2c7567cc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_6ef0316f-219a-4d57-8c2f-8efe2c7567cc_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_6ef0316f-219a-4d57-8c2f-8efe2c7567cc" xlink:to="loc_us-gaap_EquityComponentDomain_6ef0316f-219a-4d57-8c2f-8efe2c7567cc_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_d5c470db-d51c-4351-876c-b1d72bf3b582" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_6ef0316f-219a-4d57-8c2f-8efe2c7567cc" xlink:to="loc_us-gaap_EquityComponentDomain_d5c470db-d51c-4351-876c-b1d72bf3b582" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedTranslationAdjustmentMember_a4ab1b25-1355-4552-b5e6-887b4df03dab" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedTranslationAdjustmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_d5c470db-d51c-4351-876c-b1d72bf3b582" xlink:to="loc_us-gaap_AccumulatedTranslationAdjustmentMember_a4ab1b25-1355-4552-b5e6-887b4df03dab" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis_dc938363-5b75-492f-98ab-126de86ec5ef" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_58410d05-09c5-421d-b44c-7af1f9d79f0c" xlink:to="loc_srt_ConsolidationItemsAxis_dc938363-5b75-492f-98ab-126de86ec5ef" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_dc938363-5b75-492f-98ab-126de86ec5ef_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidationItemsAxis_dc938363-5b75-492f-98ab-126de86ec5ef" xlink:to="loc_srt_ConsolidationItemsDomain_dc938363-5b75-492f-98ab-126de86ec5ef_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_4a4aeb3b-efc3-4713-abbf-e25521e5c1e9" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidationItemsAxis_dc938363-5b75-492f-98ab-126de86ec5ef" xlink:to="loc_srt_ConsolidationItemsDomain_4a4aeb3b-efc3-4713-abbf-e25521e5c1e9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember_fea9a4f2-8f0d-41b0-9c75-7a68ccd15f14" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidationItemsDomain_4a4aeb3b-efc3-4713-abbf-e25521e5c1e9" xlink:to="loc_us-gaap_OperatingSegmentsMember_fea9a4f2-8f0d-41b0-9c75-7a68ccd15f14" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_a8fe73ca-1d16-4c02-ac78-bfac7a662d4b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_58410d05-09c5-421d-b44c-7af1f9d79f0c" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_a8fe73ca-1d16-4c02-ac78-bfac7a662d4b" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_a8fe73ca-1d16-4c02-ac78-bfac7a662d4b_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_a8fe73ca-1d16-4c02-ac78-bfac7a662d4b" xlink:to="loc_us-gaap_SegmentDomain_a8fe73ca-1d16-4c02-ac78-bfac7a662d4b_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_a3cff1b1-ab0d-4db1-b32c-8f3c23e6078e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_a8fe73ca-1d16-4c02-ac78-bfac7a662d4b" xlink:to="loc_us-gaap_SegmentDomain_a3cff1b1-ab0d-4db1-b32c-8f3c23e6078e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ProgramServicesSegmentMember_9e443868-5839-4041-9c82-33b73700cd97" xlink:href="kg-20250930.xsd#kg_ProgramServicesSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_a3cff1b1-ab0d-4db1-b32c-8f3c23e6078e" xlink:to="loc_kg_ProgramServicesSegmentMember_9e443868-5839-4041-9c82-33b73700cd97" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermInvestments_e7f9b339-ac2b-4a3e-9796-a5c096d82d86" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_c29bbf11-f8a3-440d-84e1-cd45e8a304f0" xlink:to="loc_us-gaap_ShortTermInvestments_e7f9b339-ac2b-4a3e-9796-a5c096d82d86" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepositContractsLiabilities_cc3520db-50aa-465e-88ba-40e9778ebf02" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepositContractsLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_c29bbf11-f8a3-440d-84e1-cd45e8a304f0" xlink:to="loc_us-gaap_DepositContractsLiabilities_cc3520db-50aa-465e-88ba-40e9778ebf02" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_93777229-5492-4846-8914-69e42290c4ec" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_c29bbf11-f8a3-440d-84e1-cd45e8a304f0" xlink:to="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_93777229-5492-4846-8914-69e42290c4ec" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_8c9d904d-f452-4c33-8eef-74f6394a32b8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_c29bbf11-f8a3-440d-84e1-cd45e8a304f0" xlink:to="loc_us-gaap_StockholdersEquity_8c9d904d-f452-4c33-8eef-74f6394a32b8" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets_b0d39638-89c2-4969-923c-e5320eb663ce" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_c29bbf11-f8a3-440d-84e1-cd45e8a304f0" xlink:to="loc_us-gaap_OtherAssets_b0d39638-89c2-4969-923c-e5320eb663ce" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/SegmentInformationScheduleofReconciliationofReportableSegmentsUnderwritingResultstoConsolidatedNetLossDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#SegmentInformationScheduleofReconciliationofReportableSegmentsUnderwritingResultstoConsolidatedNetLossDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/SegmentInformationScheduleofReconciliationofReportableSegmentsUnderwritingResultstoConsolidatedNetLossDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems_23b9428e-88be-4dbe-bcc2-2333858911e8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_eae64932-8fd4-427e-97ff-b801962be904" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_23b9428e-88be-4dbe-bcc2-2333858911e8" xlink:to="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_eae64932-8fd4-427e-97ff-b801962be904" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis_0c20ab6c-069b-4769-97d4-42400761e327" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_eae64932-8fd4-427e-97ff-b801962be904" xlink:to="loc_srt_ConsolidationItemsAxis_0c20ab6c-069b-4769-97d4-42400761e327" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_0c20ab6c-069b-4769-97d4-42400761e327_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidationItemsAxis_0c20ab6c-069b-4769-97d4-42400761e327" xlink:to="loc_srt_ConsolidationItemsDomain_0c20ab6c-069b-4769-97d4-42400761e327_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_d27c51e5-7661-4042-872d-b597a44a6e71" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidationItemsAxis_0c20ab6c-069b-4769-97d4-42400761e327" xlink:to="loc_srt_ConsolidationItemsDomain_d27c51e5-7661-4042-872d-b597a44a6e71" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember_0ff7f671-d4e6-4844-b895-ff90ce1ca141" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidationItemsDomain_d27c51e5-7661-4042-872d-b597a44a6e71" xlink:to="loc_us-gaap_OperatingSegmentsMember_0ff7f671-d4e6-4844-b895-ff90ce1ca141" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_2d17eac8-718f-479b-b678-4df0233f2aad" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_eae64932-8fd4-427e-97ff-b801962be904" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_2d17eac8-718f-479b-b678-4df0233f2aad" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_2d17eac8-718f-479b-b678-4df0233f2aad_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_2d17eac8-718f-479b-b678-4df0233f2aad" xlink:to="loc_us-gaap_SegmentDomain_2d17eac8-718f-479b-b678-4df0233f2aad_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_e09723c4-29e5-4bd7-80a9-447407f4f333" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_2d17eac8-718f-479b-b678-4df0233f2aad" xlink:to="loc_us-gaap_SegmentDomain_e09723c4-29e5-4bd7-80a9-447407f4f333" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LegacyReinsuranceSegmentMember_344c8e3c-baaa-4373-be4b-abb954ff30c2" xlink:href="kg-20250930.xsd#kg_LegacyReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_e09723c4-29e5-4bd7-80a9-447407f4f333" xlink:to="loc_kg_LegacyReinsuranceSegmentMember_344c8e3c-baaa-4373-be4b-abb954ff30c2" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ProgramServicesSegmentMember_ba89ca13-51f7-428c-a4d5-46801b6a196a" xlink:href="kg-20250930.xsd#kg_ProgramServicesSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_e09723c4-29e5-4bd7-80a9-447407f4f333" xlink:to="loc_kg_ProgramServicesSegmentMember_ba89ca13-51f7-428c-a4d5-46801b6a196a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_23b9428e-88be-4dbe-bcc2-2333858911e8" xlink:to="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenGross_88c3e5aa-cadc-433f-b682-3031ce05ae4a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsWrittenGross"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:to="loc_us-gaap_PremiumsWrittenGross_88c3e5aa-cadc-433f-b682-3031ce05ae4a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenNet_e0e7bd57-4107-428b-be37-7c2dc9dbf82f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsWrittenNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:to="loc_us-gaap_PremiumsWrittenNet_e0e7bd57-4107-428b-be37-7c2dc9dbf82f" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsEarnedNet_b1dd2f85-e90b-4cbc-9874-73e68217d54c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsEarnedNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:to="loc_us-gaap_PremiumsEarnedNet_b1dd2f85-e90b-4cbc-9874-73e68217d54c" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FeeIncome_48c92c27-2f56-441a-81d1-f40abf683447" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FeeIncome"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:to="loc_us-gaap_FeeIncome_48c92c27-2f56-441a-81d1-f40abf683447" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_438492c2-260d-46e5-8044-98c9ebf86a67" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:to="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_438492c2-260d-46e5-8044-98c9ebf86a67" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_e167235a-573c-49fb-bde7-4adbd69c2d53" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:to="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_e167235a-573c-49fb-bde7-4adbd69c2d53" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses_82511ed3-d6df-45e8-9884-cd0c8a6442a9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpenses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:to="loc_us-gaap_OperatingExpenses_82511ed3-d6df-45e8-9884-cd0c8a6442a9" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_UnderwritingIncomeLossNet_aee57126-38e0-4ffc-b3e2-5c9f86a9fb09" xlink:href="kg-20250930.xsd#kg_UnderwritingIncomeLossNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:to="loc_kg_UnderwritingIncomeLossNet_aee57126-38e0-4ffc-b3e2-5c9f86a9fb09" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:href="kg-20250930.xsd#kg_ReconciliationtoNetIncomeLossAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementAbstract_ab7fa872-9571-43be-812a-3f496861e047" xlink:to="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentIncomeAndGainLossOnInvestmentsNet_627ace40-5d74-43f3-b0c6-7bf631719d9d" xlink:href="kg-20250930.xsd#kg_InvestmentIncomeAndGainLossOnInvestmentsNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:to="loc_kg_InvestmentIncomeAndGainLossOnInvestmentsNet_627ace40-5d74-43f3-b0c6-7bf631719d9d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InterestAndAmortizationExpensesNet_16ee3cbe-a893-402b-90ae-99f1e4823cab" xlink:href="kg-20250930.xsd#kg_InterestAndAmortizationExpensesNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:to="loc_kg_InterestAndAmortizationExpensesNet_16ee3cbe-a893-402b-90ae-99f1e4823cab" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_fc5796de-e98d-433c-8ff2-a0f502f03115" xlink:href="kg-20250930.xsd#kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:to="loc_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_fc5796de-e98d-433c-8ff2-a0f502f03115" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_7aa41ec0-89df-44f2-be28-fe266ade926a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:to="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_7aa41ec0-89df-44f2-be28-fe266ade926a" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_aad1371d-de7b-43cc-9e40-582ebd171496" xlink:href="kg-20250930.xsd#kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:to="loc_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_aad1371d-de7b-43cc-9e40-582ebd171496" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherGeneralAndAdministrativeExpense_d6a69faf-9010-4f8c-85bb-e71cf44eb57d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherGeneralAndAdministrativeExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:to="loc_us-gaap_OtherGeneralAndAdministrativeExpense_d6a69faf-9010-4f8c-85bb-e71cf44eb57d" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit_d109cd5d-8f49-46fe-a0b0-c02f168bc19f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:to="loc_us-gaap_IncomeTaxExpenseBenefit_d109cd5d-8f49-46fe-a0b0-c02f168bc19f" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments_1b0d7ab0-ad0f-4efc-96f3-b62190f589c5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:to="loc_us-gaap_IncomeLossFromEquityMethodInvestments_1b0d7ab0-ad0f-4efc-96f3-b62190f589c5" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperations_50efe37a-54cd-4450-921e-a5e6a48c928d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperations"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract_ea08a4f0-2b2c-40f0-8dd3-8d0f4a3ef400" xlink:to="loc_us-gaap_IncomeLossFromContinuingOperations_50efe37a-54cd-4450-921e-a5e6a48c928d" xlink:type="arc" order="9"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/SegmentInformationScheduleofReconciliationtoConsolidatedTotalAssetsDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#SegmentInformationScheduleofReconciliationtoConsolidatedTotalAssetsDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/SegmentInformationScheduleofReconciliationtoConsolidatedTotalAssetsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingAssetReconcilingItemLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_2ac33add-35de-437a-b004-c9f0cf8881c2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_2ac33add-35de-437a-b004-c9f0cf8881c2" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis_7ca413a7-f1fd-49b8-a86b-170b0fb34a55" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_2ac33add-35de-437a-b004-c9f0cf8881c2" xlink:to="loc_srt_ConsolidationItemsAxis_7ca413a7-f1fd-49b8-a86b-170b0fb34a55" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_7ca413a7-f1fd-49b8-a86b-170b0fb34a55_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidationItemsAxis_7ca413a7-f1fd-49b8-a86b-170b0fb34a55" xlink:to="loc_srt_ConsolidationItemsDomain_7ca413a7-f1fd-49b8-a86b-170b0fb34a55_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_e74a6afe-6b7f-419c-8095-ada7488df470" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidationItemsAxis_7ca413a7-f1fd-49b8-a86b-170b0fb34a55" xlink:to="loc_srt_ConsolidationItemsDomain_e74a6afe-6b7f-419c-8095-ada7488df470" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember_4eaf04d0-2797-47f3-bfee-ec86117c6405" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidationItemsDomain_e74a6afe-6b7f-419c-8095-ada7488df470" xlink:to="loc_us-gaap_OperatingSegmentsMember_4eaf04d0-2797-47f3-bfee-ec86117c6405" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember_255b8dec-f1b7-4fcd-887c-19bb8edbf300" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidationItemsDomain_e74a6afe-6b7f-419c-8095-ada7488df470" xlink:to="loc_us-gaap_CorporateNonSegmentMember_255b8dec-f1b7-4fcd-887c-19bb8edbf300" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_f5d68d38-88e3-41f3-a145-dd895b61f019" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_2ac33add-35de-437a-b004-c9f0cf8881c2" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_f5d68d38-88e3-41f3-a145-dd895b61f019" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_f5d68d38-88e3-41f3-a145-dd895b61f019_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_f5d68d38-88e3-41f3-a145-dd895b61f019" xlink:to="loc_us-gaap_SegmentDomain_f5d68d38-88e3-41f3-a145-dd895b61f019_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_c8d6d0cf-5f6e-463b-b281-a665c908732b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_f5d68d38-88e3-41f3-a145-dd895b61f019" xlink:to="loc_us-gaap_SegmentDomain_c8d6d0cf-5f6e-463b-b281-a665c908732b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LegacyReinsuranceSegmentMember_1bb5226e-7d76-405d-822e-32c76442b668" xlink:href="kg-20250930.xsd#kg_LegacyReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_c8d6d0cf-5f6e-463b-b281-a665c908732b" xlink:to="loc_kg_LegacyReinsuranceSegmentMember_1bb5226e-7d76-405d-822e-32c76442b668" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ProgramServicesSegmentMember_d3c392d6-8690-46d5-91a0-9eb0913574f7" xlink:href="kg-20250930.xsd#kg_ProgramServicesSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_c8d6d0cf-5f6e-463b-b281-a665c908732b" xlink:to="loc_kg_ProgramServicesSegmentMember_d3c392d6-8690-46d5-91a0-9eb0913574f7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_a818134a-354b-4674-b0fb-eef45f2163bc" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_2ac33add-35de-437a-b004-c9f0cf8881c2" xlink:to="loc_srt_RangeAxis_a818134a-354b-4674-b0fb-eef45f2163bc" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_a818134a-354b-4674-b0fb-eef45f2163bc_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_a818134a-354b-4674-b0fb-eef45f2163bc" xlink:to="loc_srt_RangeMember_a818134a-354b-4674-b0fb-eef45f2163bc_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_dffb4ed6-c8bd-4b4d-a717-d8431d63f3b4" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_a818134a-354b-4674-b0fb-eef45f2163bc" xlink:to="loc_srt_RangeMember_dffb4ed6-c8bd-4b4d-a717-d8431d63f3b4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember_2b21804f-e2b7-4ed2-b619-edf1a777035a" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_dffb4ed6-c8bd-4b4d-a717-d8431d63f3b4" xlink:to="loc_srt_MinimumMember_2b21804f-e2b7-4ed2-b619-edf1a777035a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_87ac72e0-9678-482d-8a7c-983ccfa7d3f7" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_dffb4ed6-c8bd-4b4d-a717-d8431d63f3b4" xlink:to="loc_srt_MaximumMember_87ac72e0-9678-482d-8a7c-983ccfa7d3f7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAtCarryingValue_4fade901-650d-410a-8dcc-e0d5e36e3fb7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsReceivableAtCarryingValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_PremiumsReceivableAtCarryingValue_4fade901-650d-410a-8dcc-e0d5e36e3fb7" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_6d7fb91e-639b-4e56-b491-a9a15ffe2526" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_6d7fb91e-639b-4e56-b491-a9a15ffe2526" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCosts_4d2cb11b-cb67-43f7-b040-d6f1d45c7e4a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredPolicyAcquisitionCosts"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_DeferredPolicyAcquisitionCosts_4d2cb11b-cb67-43f7-b040-d6f1d45c7e4a" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableRelatedParties_b1e3d25e-e6dd-45c1-8e59-8b83f1308ca1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableRelatedParties"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_LoansAndLeasesReceivableRelatedParties_b1e3d25e-e6dd-45c1-8e59-8b83f1308ca1" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetIncludingGoodwill_ffd8447a-6566-4dcf-b0ef-e65d14c7b68f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetIncludingGoodwill"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_IntangibleAssetsNetIncludingGoodwill_ffd8447a-6566-4dcf-b0ef-e65d14c7b68f" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndInvestments_af16421d-41ed-44f7-89fb-0497de47caa8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_RestrictedCashAndInvestments_af16421d-41ed-44f7-89fb-0497de47caa8" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset_32724a31-6fb0-4062-86c4-6e2e569f533b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FundsHeldUnderReinsuranceAgreementsAsset"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset_32724a31-6fb0-4062-86c4-6e2e569f533b" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets_3ccd6061-b0d8-49f7-8bf1-e53e4b2b3d89" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_OtherAssets_3ccd6061-b0d8-49f7-8bf1-e53e4b2b3d89" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_da2f8a63-89ad-4368-bbb4-c3a7212b82ae" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_da2f8a63-89ad-4368-bbb4-c3a7212b82ae" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets_90855e8d-fc1c-432e-9399-faa2f63c9ce4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_us-gaap_Assets_90855e8d-fc1c-432e-9399-faa2f63c9ce4" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod_f03602df-2208-46af-8450-fe9f75edffe0" xlink:href="kg-20250930.xsd#kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems_89212f0e-296f-4923-b0c5-30e8ecedca3f" xlink:to="loc_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod_f03602df-2208-46af-8450-fe9f75edffe0" xlink:type="arc" order="10"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/SegmentInformationScheduleofNetPremiumsbyMajorLineofBusinessDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#SegmentInformationScheduleofNetPremiumsbyMajorLineofBusinessDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/SegmentInformationScheduleofNetPremiumsbyMajorLineofBusinessDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingRevenueReconcilingItemLineItems_2197855d-9ff4-40dd-b7b7-8e66b0397dc6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingRevenueReconcilingItemLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable_a70cc5bd-9f27-470c-93a7-c4afff22a8f0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_SegmentReportingRevenueReconcilingItemLineItems_2197855d-9ff4-40dd-b7b7-8e66b0397dc6" xlink:to="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable_a70cc5bd-9f27-470c-93a7-c4afff22a8f0" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_7022b114-6925-4636-a855-ba5808dd077b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable_a70cc5bd-9f27-470c-93a7-c4afff22a8f0" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_7022b114-6925-4636-a855-ba5808dd077b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_7022b114-6925-4636-a855-ba5808dd077b_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_7022b114-6925-4636-a855-ba5808dd077b" xlink:to="loc_us-gaap_SegmentDomain_7022b114-6925-4636-a855-ba5808dd077b_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_a4463923-193f-4c01-94d5-6cf525688311" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_7022b114-6925-4636-a855-ba5808dd077b" xlink:to="loc_us-gaap_SegmentDomain_a4463923-193f-4c01-94d5-6cf525688311" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DiversifiedLegacySegmentMember_081a2dc6-35d0-43ed-818d-806093879ed5" xlink:href="kg-20250930.xsd#kg_DiversifiedLegacySegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_a4463923-193f-4c01-94d5-6cf525688311" xlink:to="loc_kg_DiversifiedLegacySegmentMember_081a2dc6-35d0-43ed-818d-806093879ed5" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustLegacySegmentMember_31bce01d-9d57-426d-8180-829458581695" xlink:href="kg-20250930.xsd#kg_AmTrustLegacySegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_a4463923-193f-4c01-94d5-6cf525688311" xlink:to="loc_kg_AmTrustLegacySegmentMember_31bce01d-9d57-426d-8180-829458581695" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LegacyReinsuranceSegmentMember_814133c7-e07b-4ef2-b4ef-6a9e0ec2a460" xlink:href="kg-20250930.xsd#kg_LegacyReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_a4463923-193f-4c01-94d5-6cf525688311" xlink:to="loc_kg_LegacyReinsuranceSegmentMember_814133c7-e07b-4ef2-b4ef-6a9e0ec2a460" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis_2ed5553e-1b96-4ba7-8e09-6ce0a0de3f36" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable_a70cc5bd-9f27-470c-93a7-c4afff22a8f0" xlink:to="loc_srt_ConsolidationItemsAxis_2ed5553e-1b96-4ba7-8e09-6ce0a0de3f36" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_2ed5553e-1b96-4ba7-8e09-6ce0a0de3f36_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidationItemsAxis_2ed5553e-1b96-4ba7-8e09-6ce0a0de3f36" xlink:to="loc_srt_ConsolidationItemsDomain_2ed5553e-1b96-4ba7-8e09-6ce0a0de3f36_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_98d938ab-758b-4cb3-98f1-f4aff668df9d" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidationItemsAxis_2ed5553e-1b96-4ba7-8e09-6ce0a0de3f36" xlink:to="loc_srt_ConsolidationItemsDomain_98d938ab-758b-4cb3-98f1-f4aff668df9d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember_ee771e4c-534e-40ce-9bc4-8a325bac5c5d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidationItemsDomain_98d938ab-758b-4cb3-98f1-f4aff668df9d" xlink:to="loc_us-gaap_OperatingSegmentsMember_ee771e4c-534e-40ce-9bc4-8a325bac5c5d" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenNet_7a79f712-772e-4c43-80cd-ec62fce08348" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsWrittenNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingRevenueReconcilingItemLineItems_2197855d-9ff4-40dd-b7b7-8e66b0397dc6" xlink:to="loc_us-gaap_PremiumsWrittenNet_7a79f712-772e-4c43-80cd-ec62fce08348" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsEarnedNet_c4d1e389-6c94-4beb-bbef-6e5a27b78e23" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsEarnedNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingRevenueReconcilingItemLineItems_2197855d-9ff4-40dd-b7b7-8e66b0397dc6" xlink:to="loc_us-gaap_PremiumsEarnedNet_c4d1e389-6c94-4beb-bbef-6e5a27b78e23" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofAmortizedCostGrossUnrealizedGainsandLossesandFairValueonFixedMaturitiesDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofAmortizedCostGrossUnrealizedGainsandLossesandFairValueonFixedMaturitiesDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofAmortizedCostGrossUnrealizedGainsandLossesandFairValueonFixedMaturitiesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsLineItems_7ca456fd-86ae-4851-9bda-3634f08576ff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsTable_b2779d31-d8ed-43e6-828e-6711b81e1ea0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_7ca456fd-86ae-4851-9bda-3634f08576ff" xlink:to="loc_us-gaap_ScheduleOfInvestmentsTable_b2779d31-d8ed-43e6-828e-6711b81e1ea0" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_102ea93c-ad39-4579-ba2c-dde144fd9956" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentsTable_b2779d31-d8ed-43e6-828e-6711b81e1ea0" xlink:to="loc_us-gaap_FinancialInstrumentAxis_102ea93c-ad39-4579-ba2c-dde144fd9956" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_102ea93c-ad39-4579-ba2c-dde144fd9956_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_102ea93c-ad39-4579-ba2c-dde144fd9956" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_102ea93c-ad39-4579-ba2c-dde144fd9956_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4275cb61-1e99-4f25-9aac-d9f1685e314f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_102ea93c-ad39-4579-ba2c-dde144fd9956" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4275cb61-1e99-4f25-9aac-d9f1685e314f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryBondSecuritiesMember_f2fb1211-cae9-4c41-bf87-48228a655aa9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USTreasuryBondSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4275cb61-1e99-4f25-9aac-d9f1685e314f" xlink:to="loc_us-gaap_USTreasuryBondSecuritiesMember_f2fb1211-cae9-4c41-bf87-48228a655aa9" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_996f0945-4c32-40b7-9253-b9e5911ec1cc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4275cb61-1e99-4f25-9aac-d9f1685e314f" xlink:to="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_996f0945-4c32-40b7-9253-b9e5911ec1cc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignGovernmentDebtMember_b5516ea8-e104-4b35-b021-eca05cbb778d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignGovernmentDebtMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4275cb61-1e99-4f25-9aac-d9f1685e314f" xlink:to="loc_us-gaap_ForeignGovernmentDebtMember_b5516ea8-e104-4b35-b021-eca05cbb778d" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralizedLoanObligationsMember_b867a2ca-c67b-492b-b0f3-ecb5b44f2e86" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CollateralizedLoanObligationsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4275cb61-1e99-4f25-9aac-d9f1685e314f" xlink:to="loc_us-gaap_CollateralizedLoanObligationsMember_b867a2ca-c67b-492b-b0f3-ecb5b44f2e86" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateBondSecuritiesMember_c00de96f-18e5-4f5a-a7a5-5f546402a1c9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateBondSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4275cb61-1e99-4f25-9aac-d9f1685e314f" xlink:to="loc_us-gaap_CorporateBondSecuritiesMember_c00de96f-18e5-4f5a-a7a5-5f546402a1c9" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_13f10ad1-2faa-4943-9e84-f2f48b9cc916" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_7ca456fd-86ae-4851-9bda-3634f08576ff" xlink:to="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_13f10ad1-2faa-4943-9e84-f2f48b9cc916" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_ac867f53-e04d-4406-acad-a938f30ba7ed" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_7ca456fd-86ae-4851-9bda-3634f08576ff" xlink:to="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_ac867f53-e04d-4406-acad-a938f30ba7ed" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_d1ffc126-e471-4039-b07a-fddd2943169e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_7ca456fd-86ae-4851-9bda-3634f08576ff" xlink:to="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_d1ffc126-e471-4039-b07a-fddd2943169e" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities_d7efc46a-3d07-4fd5-83e0-ca7f4603bf0f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_7ca456fd-86ae-4851-9bda-3634f08576ff" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities_d7efc46a-3d07-4fd5-83e0-ca7f4603bf0f" xlink:type="arc" order="3"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsNarrativeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_dcd3ca5c-3103-4cc9-84eb-7a252bd7c2e9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_dcd3ca5c-3103-4cc9-84eb-7a252bd7c2e9" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis_83670a44-992a-453e-8d69-c1f625c96e2c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_dcd3ca5c-3103-4cc9-84eb-7a252bd7c2e9" xlink:to="loc_us-gaap_InvestmentTypeAxis_83670a44-992a-453e-8d69-c1f625c96e2c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_83670a44-992a-453e-8d69-c1f625c96e2c_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_InvestmentTypeAxis_83670a44-992a-453e-8d69-c1f625c96e2c" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_83670a44-992a-453e-8d69-c1f625c96e2c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_a1179ac3-3815-4450-b655-438c026082f0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_InvestmentTypeAxis_83670a44-992a-453e-8d69-c1f625c96e2c" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_a1179ac3-3815-4450-b655-438c026082f0" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DirectLendingEntitiesMember_2c85b90e-e214-4e57-b720-b281fcce99ac" xlink:href="kg-20250930.xsd#kg_DirectLendingEntitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_a1179ac3-3815-4450-b655-438c026082f0" xlink:to="loc_kg_DirectLendingEntitiesMember_2c85b90e-e214-4e57-b720-b281fcce99ac" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable_02f73a9a-5942-4090-ad41-82ffc44d7c25" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestReceivable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:to="loc_us-gaap_InterestReceivable_02f73a9a-5942-4090-ad41-82ffc44d7c25" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestWriteoff_9f66d4cf-c579-45b6-8f95-1eba18b4d03a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAccruedInterestWriteoff"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:to="loc_us-gaap_FinancingReceivableAccruedInterestWriteoff_9f66d4cf-c579-45b6-8f95-1eba18b4d03a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions_c55e3717-1f4b-428e-b3fd-2cfe7635be97" xlink:href="kg-20250930.xsd#kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:to="loc_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions_c55e3717-1f4b-428e-b3fd-2cfe7635be97" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsContinuousUnrealizedLossPositionFairValue_4c267776-1bfe-4189-8321-4380ea92edbb" xlink:href="kg-20250930.xsd#kg_InvestmentsContinuousUnrealizedLossPositionFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:to="loc_kg_InvestmentsContinuousUnrealizedLossPositionFairValue_4c267776-1bfe-4189-8321-4380ea92edbb" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss_76a2c65b-e0cd-4961-8c99-91d4f27000c9" xlink:href="kg-20250930.xsd#kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:to="loc_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss_76a2c65b-e0cd-4961-8c99-91d4f27000c9" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_7a2cb9ff-53bf-4282-a1dc-8eb7a2a566ed" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_7a2cb9ff-53bf-4282-a1dc-8eb7a2a566ed" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestments_fee8f4ab-fec2-4eb2-8512-d7a70fdf0ef9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:to="loc_us-gaap_OtherInvestments_fee8f4ab-fec2-4eb2-8512-d7a70fdf0ef9" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_c7b5c631-dd95-4be2-b58b-d3aa39751e4b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_278cf8e1-91bf-4ee4-8c07-a4b4c0b1ddfc" xlink:to="loc_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_c7b5c631-dd95-4be2-b58b-d3aa39751e4b" xlink:type="arc" order="7"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofContractualMaturitiesofFixedMaturitiesDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofContractualMaturitiesofFixedMaturitiesDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofContractualMaturitiesofFixedMaturitiesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsLineItems_26227ff0-9b79-42f9-bd54-1d5b90c48b1d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_a24973cb-0443-4afc-9b44-de507ea41bb0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_26227ff0-9b79-42f9-bd54-1d5b90c48b1d" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_a24973cb-0443-4afc-9b44-de507ea41bb0" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_3896a1a1-42a3-4ba3-82d9-20e73866baa0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_a24973cb-0443-4afc-9b44-de507ea41bb0" xlink:to="loc_us-gaap_FinancialInstrumentAxis_3896a1a1-42a3-4ba3-82d9-20e73866baa0" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_3896a1a1-42a3-4ba3-82d9-20e73866baa0_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_3896a1a1-42a3-4ba3-82d9-20e73866baa0" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_3896a1a1-42a3-4ba3-82d9-20e73866baa0_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_332e09d1-5a08-4d4a-883c-2554be508eed" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_3896a1a1-42a3-4ba3-82d9-20e73866baa0" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_332e09d1-5a08-4d4a-883c-2554be508eed" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_13877d9b-5e40-478c-b7a3-f10c0e74d9d2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_332e09d1-5a08-4d4a-883c-2554be508eed" xlink:to="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_13877d9b-5e40-478c-b7a3-f10c0e74d9d2" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralizedLoanObligationsMember_831813ec-9f4f-4aa8-b500-4b686abc04ef" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CollateralizedLoanObligationsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_332e09d1-5a08-4d4a-883c-2554be508eed" xlink:to="loc_us-gaap_CollateralizedLoanObligationsMember_831813ec-9f4f-4aa8-b500-4b686abc04ef" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_833276f7-b94e-49d0-8250-cea8c6045f30" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_26227ff0-9b79-42f9-bd54-1d5b90c48b1d" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_833276f7-b94e-49d0-8250-cea8c6045f30" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_36a3b3e4-3fe3-4635-a757-f5a6dd1446a6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_833276f7-b94e-49d0-8250-cea8c6045f30" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_36a3b3e4-3fe3-4635-a757-f5a6dd1446a6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_d989cbe7-c2e6-4d47-af2e-3e55e84904c5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_833276f7-b94e-49d0-8250-cea8c6045f30" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_d989cbe7-c2e6-4d47-af2e-3e55e84904c5" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_2c481de6-378d-4aa8-972a-a4507a4a2da7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_833276f7-b94e-49d0-8250-cea8c6045f30" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_2c481de6-378d-4aa8-972a-a4507a4a2da7" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_52681447-358c-4e4f-824b-7512d7d042c8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_833276f7-b94e-49d0-8250-cea8c6045f30" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_52681447-358c-4e4f-824b-7512d7d042c8" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost_6fd9121f-f06f-424e-bff7-d5424991a548" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_833276f7-b94e-49d0-8250-cea8c6045f30" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost_6fd9121f-f06f-424e-bff7-d5424991a548" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_f7fa7ab9-a79a-4600-9837-9367b8ad53af" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_833276f7-b94e-49d0-8250-cea8c6045f30" xlink:to="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_f7fa7ab9-a79a-4600-9837-9367b8ad53af" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_a2f1ae2f-9a4c-41c7-8019-2637e557e59e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_26227ff0-9b79-42f9-bd54-1d5b90c48b1d" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_a2f1ae2f-9a4c-41c7-8019-2637e557e59e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_c4ca4fef-81d1-4c50-9c66-9154faa7ddcf" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_a2f1ae2f-9a4c-41c7-8019-2637e557e59e" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_c4ca4fef-81d1-4c50-9c66-9154faa7ddcf" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_d3bfe799-aff4-4a6f-816a-fe2edf981640" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_a2f1ae2f-9a4c-41c7-8019-2637e557e59e" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_d3bfe799-aff4-4a6f-816a-fe2edf981640" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_4a79d88a-5186-423b-84da-d197adc3239c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_a2f1ae2f-9a4c-41c7-8019-2637e557e59e" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_4a79d88a-5186-423b-84da-d197adc3239c" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_b12c4a21-35fc-4ff6-88c0-cc9d7a618a0d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_a2f1ae2f-9a4c-41c7-8019-2637e557e59e" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_b12c4a21-35fc-4ff6-88c0-cc9d7a618a0d" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_2eb9e2a6-56a4-4610-abfd-385c9d0c2587" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_a2f1ae2f-9a4c-41c7-8019-2637e557e59e" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_2eb9e2a6-56a4-4610-abfd-385c9d0c2587" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities_88a72173-1366-42f4-b03d-74b40b3757e9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_a2f1ae2f-9a4c-41c7-8019-2637e557e59e" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities_88a72173-1366-42f4-b03d-74b40b3757e9" xlink:type="arc" order="6"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofFixedMaturitiesinanUnrealizedLossPositionandAggregateFairValueDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofFixedMaturitiesinanUnrealizedLossPositionandAggregateFairValueDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofFixedMaturitiesinanUnrealizedLossPositionandAggregateFairValueDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_241e99cc-5bf7-48d1-a95c-8553f239da37" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_2930387d-685c-4c15-abf8-5f6120e0d19c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_241e99cc-5bf7-48d1-a95c-8553f239da37" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_2930387d-685c-4c15-abf8-5f6120e0d19c" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_d332960c-197b-40d4-ae07-62e94e742b6d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_2930387d-685c-4c15-abf8-5f6120e0d19c" xlink:to="loc_us-gaap_FinancialInstrumentAxis_d332960c-197b-40d4-ae07-62e94e742b6d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_d332960c-197b-40d4-ae07-62e94e742b6d_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_d332960c-197b-40d4-ae07-62e94e742b6d" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_d332960c-197b-40d4-ae07-62e94e742b6d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_81ecf033-a3ac-456b-bbe4-7dad5618cf27" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_d332960c-197b-40d4-ae07-62e94e742b6d" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_81ecf033-a3ac-456b-bbe4-7dad5618cf27" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignGovernmentDebtMember_90b954fc-929e-4a64-a5f6-74f3b8612afc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignGovernmentDebtMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_81ecf033-a3ac-456b-bbe4-7dad5618cf27" xlink:to="loc_us-gaap_ForeignGovernmentDebtMember_90b954fc-929e-4a64-a5f6-74f3b8612afc" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralizedLoanObligationsMember_04f69ed8-e3f1-4f0b-94dc-dc9e4b1a6535" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CollateralizedLoanObligationsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_81ecf033-a3ac-456b-bbe4-7dad5618cf27" xlink:to="loc_us-gaap_CollateralizedLoanObligationsMember_04f69ed8-e3f1-4f0b-94dc-dc9e4b1a6535" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract_572d7209-1fa3-45a4-a7ac-d9116c7a30e9" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_241e99cc-5bf7-48d1-a95c-8553f239da37" xlink:to="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract_572d7209-1fa3-45a4-a7ac-d9116c7a30e9" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue_c5426e85-9780-4373-8de2-a7db394fa0d6" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract_572d7209-1fa3-45a4-a7ac-d9116c7a30e9" xlink:to="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue_c5426e85-9780-4373-8de2-a7db394fa0d6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue_ca19ea6a-88a7-4788-91da-24c067a68360" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract_572d7209-1fa3-45a4-a7ac-d9116c7a30e9" xlink:to="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue_ca19ea6a-88a7-4788-91da-24c067a68360" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue_c252cc29-0008-466f-aa31-74597ac41830" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract_572d7209-1fa3-45a4-a7ac-d9116c7a30e9" xlink:to="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue_c252cc29-0008-466f-aa31-74597ac41830" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_4fca83fd-6052-4f49-94c5-1b92a0394608" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_241e99cc-5bf7-48d1-a95c-8553f239da37" xlink:to="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_4fca83fd-6052-4f49-94c5-1b92a0394608" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss_3cd02c79-5a83-4ef5-9ee4-9a6488ee574b" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_4fca83fd-6052-4f49-94c5-1b92a0394608" xlink:to="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss_3cd02c79-5a83-4ef5-9ee4-9a6488ee574b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss_b2b65e19-ec80-4386-9ae7-037f95a36ccb" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_4fca83fd-6052-4f49-94c5-1b92a0394608" xlink:to="loc_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss_b2b65e19-ec80-4386-9ae7-037f95a36ccb" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss_18bd5e06-7d1f-43dc-af7e-532d8e637f4e" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_4fca83fd-6052-4f49-94c5-1b92a0394608" xlink:to="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss_18bd5e06-7d1f-43dc-af7e-532d8e637f4e" xlink:type="arc" order="3"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleoftheCreditRatingsofFixedMaturitiesDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleoftheCreditRatingsofFixedMaturitiesDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleoftheCreditRatingsofFixedMaturitiesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleofFixedMaturitiesTableLineItems_75b22ab2-c1c5-4a88-914e-1c5b68f8a504" xlink:href="kg-20250930.xsd#kg_ScheduleofFixedMaturitiesTableLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleofFixedMaturitiesTable_7f6ea836-06c7-4454-83c5-b0de7aa2eb8f" xlink:href="kg-20250930.xsd#kg_ScheduleofFixedMaturitiesTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_kg_ScheduleofFixedMaturitiesTableLineItems_75b22ab2-c1c5-4a88-914e-1c5b68f8a504" xlink:to="loc_kg_ScheduleofFixedMaturitiesTable_7f6ea836-06c7-4454-83c5-b0de7aa2eb8f" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_faaa42a6-996d-41b6-8c2b-920849b9f36d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_kg_ScheduleofFixedMaturitiesTable_7f6ea836-06c7-4454-83c5-b0de7aa2eb8f" xlink:to="loc_us-gaap_FinancialInstrumentAxis_faaa42a6-996d-41b6-8c2b-920849b9f36d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_faaa42a6-996d-41b6-8c2b-920849b9f36d_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_faaa42a6-996d-41b6-8c2b-920849b9f36d" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_faaa42a6-996d-41b6-8c2b-920849b9f36d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_e93b09e0-0523-487e-bd32-4ca3aeca6318" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_faaa42a6-996d-41b6-8c2b-920849b9f36d" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_e93b09e0-0523-487e-bd32-4ca3aeca6318" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasurySecuritiesMember_98e707ab-df67-4e42-8885-bcf4f1aa9329" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USTreasurySecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_e93b09e0-0523-487e-bd32-4ca3aeca6318" xlink:to="loc_us-gaap_USTreasurySecuritiesMember_98e707ab-df67-4e42-8885-bcf4f1aa9329" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_0a448732-dda3-4183-a553-a16d1f62ea58" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USGovernmentAgenciesDebtSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_e93b09e0-0523-487e-bd32-4ca3aeca6318" xlink:to="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_0a448732-dda3-4183-a553-a16d1f62ea58" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CreditRatingStandardPoorsAxis_5fb32cfe-a90e-44aa-8850-4ac1e062e523" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CreditRatingStandardPoorsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_kg_ScheduleofFixedMaturitiesTable_7f6ea836-06c7-4454-83c5-b0de7aa2eb8f" xlink:to="loc_srt_CreditRatingStandardPoorsAxis_5fb32cfe-a90e-44aa-8850-4ac1e062e523" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ExternalCreditRatingStandardPoorsMember_5fb32cfe-a90e-44aa-8850-4ac1e062e523_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ExternalCreditRatingStandardPoorsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_CreditRatingStandardPoorsAxis_5fb32cfe-a90e-44aa-8850-4ac1e062e523" xlink:to="loc_srt_ExternalCreditRatingStandardPoorsMember_5fb32cfe-a90e-44aa-8850-4ac1e062e523_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ExternalCreditRatingStandardPoorsMember_aae5e38f-4212-437a-aeba-7f3d4e8bd9c7" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ExternalCreditRatingStandardPoorsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_CreditRatingStandardPoorsAxis_5fb32cfe-a90e-44aa-8850-4ac1e062e523" xlink:to="loc_srt_ExternalCreditRatingStandardPoorsMember_aae5e38f-4212-437a-aeba-7f3d4e8bd9c7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StandardPoorsAAARatingMember_0e6ba617-fddb-4a68-96ce-5a32c451bf53" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsAAARatingMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ExternalCreditRatingStandardPoorsMember_aae5e38f-4212-437a-aeba-7f3d4e8bd9c7" xlink:to="loc_srt_StandardPoorsAAARatingMember_0e6ba617-fddb-4a68-96ce-5a32c451bf53" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_StandardPoorsAaPlusAaAaMinusRatingMember_a99ff752-1385-4b9d-a9a3-ff6597235fba" xlink:href="kg-20250930.xsd#kg_StandardPoorsAaPlusAaAaMinusRatingMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ExternalCreditRatingStandardPoorsMember_aae5e38f-4212-437a-aeba-7f3d4e8bd9c7" xlink:to="loc_kg_StandardPoorsAaPlusAaAaMinusRatingMember_a99ff752-1385-4b9d-a9a3-ff6597235fba" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember_39a23593-af39-4148-aee2-18c03a83a960" xlink:href="kg-20250930.xsd#kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ExternalCreditRatingStandardPoorsMember_aae5e38f-4212-437a-aeba-7f3d4e8bd9c7" xlink:to="loc_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember_39a23593-af39-4148-aee2-18c03a83a960" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember_f66d5d6e-1fca-489a-8222-58d7e012f0c4" xlink:href="kg-20250930.xsd#kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ExternalCreditRatingStandardPoorsMember_aae5e38f-4212-437a-aeba-7f3d4e8bd9c7" xlink:to="loc_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember_f66d5d6e-1fca-489a-8222-58d7e012f0c4" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesAmortizedCostBasis_33250db2-2334-44ff-bbf7-5c4962d15e0c" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesAmortizedCostBasis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ScheduleofFixedMaturitiesTableLineItems_75b22ab2-c1c5-4a88-914e-1c5b68f8a504" xlink:to="loc_kg_FixedMaturitiesAmortizedCostBasis_33250db2-2334-44ff-bbf7-5c4962d15e0c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesFairValue_0fabdda3-a35a-4950-9bf4-bb4e4eefcc99" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ScheduleofFixedMaturitiesTableLineItems_75b22ab2-c1c5-4a88-914e-1c5b68f8a504" xlink:to="loc_kg_FixedMaturitiesFairValue_0fabdda3-a35a-4950-9bf4-bb4e4eefcc99" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesPercentofTotalFairValue_ca786e3c-8bda-44d6-8ec7-2227353e3c3e" xlink:href="kg-20250930.xsd#kg_FixedMaturitiesPercentofTotalFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_ScheduleofFixedMaturitiesTableLineItems_75b22ab2-c1c5-4a88-914e-1c5b68f8a504" xlink:to="loc_kg_FixedMaturitiesPercentofTotalFairValue_ca786e3c-8bda-44d6-8ec7-2227353e3c3e" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofCompositionofOtherInvestmentsDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofCompositionofOtherInvestmentsDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofCompositionofOtherInvestmentsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsLineItems_4ccb6edb-ffa2-4e03-847a-9b52f1605033" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsTable_d016b63d-7908-434b-b45b-da42116c0064" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_4ccb6edb-ffa2-4e03-847a-9b52f1605033" xlink:to="loc_us-gaap_ScheduleOfInvestmentsTable_d016b63d-7908-434b-b45b-da42116c0064" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis_318390e4-00fa-4184-98b1-503389cda989" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentsTable_d016b63d-7908-434b-b45b-da42116c0064" xlink:to="loc_us-gaap_InvestmentTypeAxis_318390e4-00fa-4184-98b1-503389cda989" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_318390e4-00fa-4184-98b1-503389cda989_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_InvestmentTypeAxis_318390e4-00fa-4184-98b1-503389cda989" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_318390e4-00fa-4184-98b1-503389cda989_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_328caabb-5dc4-4134-8406-d882c82c795f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_InvestmentTypeAxis_318390e4-00fa-4184-98b1-503389cda989" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_328caabb-5dc4-4134-8406-d882c82c795f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrivateEquityFundsMember_30e57d5e-6484-4bad-851f-56dc61db7d92" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrivateEquityFundsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_328caabb-5dc4-4134-8406-d882c82c795f" xlink:to="loc_us-gaap_PrivateEquityFundsMember_30e57d5e-6484-4bad-851f-56dc61db7d92" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherPrivatelyHeldInvestmentsMember_a8a8d44a-19f2-4a6d-8328-2daf42cd1c14" xlink:href="kg-20250930.xsd#kg_OtherPrivatelyHeldInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_328caabb-5dc4-4134-8406-d882c82c795f" xlink:to="loc_kg_OtherPrivatelyHeldInvestmentsMember_a8a8d44a-19f2-4a6d-8328-2daf42cd1c14" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivateCreditLendingMember_cfefc2db-fc37-490a-9269-d5090bb96c88" xlink:href="kg-20250930.xsd#kg_PrivateCreditLendingMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_328caabb-5dc4-4134-8406-d882c82c795f" xlink:to="loc_kg_PrivateCreditLendingMember_cfefc2db-fc37-490a-9269-d5090bb96c88" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsMember_6908cba1-eff7-4603-aa0b-537d080c8adc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_328caabb-5dc4-4134-8406-d882c82c795f" xlink:to="loc_us-gaap_EquityMethodInvestmentsMember_6908cba1-eff7-4603-aa0b-537d080c8adc" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DirectLendingEntitiesMember_37770e78-7a3e-4ac4-97fa-db4f91ac762a" xlink:href="kg-20250930.xsd#kg_DirectLendingEntitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_328caabb-5dc4-4134-8406-d882c82c795f" xlink:to="loc_kg_DirectLendingEntitiesMember_37770e78-7a3e-4ac4-97fa-db4f91ac762a" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestments_e1cf576b-a3f4-494b-ba58-b5cc04b54f46" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_4ccb6edb-ffa2-4e03-847a-9b52f1605033" xlink:to="loc_us-gaap_OtherInvestments_e1cf576b-a3f4-494b-ba58-b5cc04b54f46" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentsPercentOfTotal_dc2d888d-a568-4bcc-b82e-9bbda3dfc39c" xlink:href="kg-20250930.xsd#kg_OtherInvestmentsPercentOfTotal"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_4ccb6edb-ffa2-4e03-847a-9b52f1605033" xlink:to="loc_kg_OtherInvestmentsPercentOfTotal_dc2d888d-a568-4bcc-b82e-9bbda3dfc39c" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofCostandFairValuesoftheEquitySecuritiesDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofCostandFairValuesoftheEquitySecuritiesDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofCostandFairValuesoftheEquitySecuritiesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_53d5d9cd-e816-4b34-9738-2b6fb713f068" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_1f770285-64d9-404e-9015-b463008e4c7a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_53d5d9cd-e816-4b34-9738-2b6fb713f068" xlink:to="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_1f770285-64d9-404e-9015-b463008e4c7a" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis_65ca96c5-4029-4034-bdc7-cf32146926df" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_1f770285-64d9-404e-9015-b463008e4c7a" xlink:to="loc_us-gaap_InvestmentTypeAxis_65ca96c5-4029-4034-bdc7-cf32146926df" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_65ca96c5-4029-4034-bdc7-cf32146926df_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_InvestmentTypeAxis_65ca96c5-4029-4034-bdc7-cf32146926df" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_65ca96c5-4029-4034-bdc7-cf32146926df_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_8d7b9e2e-61bb-4751-baba-aff4ac0bea9a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_InvestmentTypeAxis_65ca96c5-4029-4034-bdc7-cf32146926df" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_8d7b9e2e-61bb-4751-baba-aff4ac0bea9a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquitySecuritiesInCommonStockMember_297d2ed2-4853-4ff6-9de9-0c6f3f52fcb4" xlink:href="kg-20250930.xsd#kg_PrivatelyHeldEquitySecuritiesInCommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_8d7b9e2e-61bb-4751-baba-aff4ac0bea9a" xlink:to="loc_kg_PrivatelyHeldEquitySecuritiesInCommonStockMember_297d2ed2-4853-4ff6-9de9-0c6f3f52fcb4" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember_8b8d1c29-597e-4ce2-9787-293bb02de575" xlink:href="kg-20250930.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_8d7b9e2e-61bb-4751-baba-aff4ac0bea9a" xlink:to="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember_8b8d1c29-597e-4ce2-9787-293bb02de575" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiCost_ce319ece-5097-4e54-a017-938ce3fabe40" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_53d5d9cd-e816-4b34-9738-2b6fb713f068" xlink:to="loc_us-gaap_EquitySecuritiesFvNiCost_ce319ece-5097-4e54-a017-938ce3fabe40" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNi_c3734180-7ebd-4192-ae55-5eb6496178f5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNi"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_53d5d9cd-e816-4b34-9738-2b6fb713f068" xlink:to="loc_us-gaap_EquitySecuritiesFvNi_c3734180-7ebd-4192-ae55-5eb6496178f5" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofPrivatelyHeldSecuritiesHeldSubjecttoContractualSaleRestrictionsDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofPrivatelyHeldSecuritiesHeldSubjecttoContractualSaleRestrictionsDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofPrivatelyHeldSecuritiesHeldSubjecttoContractualSaleRestrictionsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_b1deeb9f-3524-4f79-bcb5-a4d12a14a735" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_fcd934df-9ef2-434c-b5c1-465a826f0b88" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_b1deeb9f-3524-4f79-bcb5-a4d12a14a735" xlink:to="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_fcd934df-9ef2-434c-b5c1-465a826f0b88" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_91d586fa-1a6c-4fe1-a6eb-cc79da42aafb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_fcd934df-9ef2-434c-b5c1-465a826f0b88" xlink:to="loc_us-gaap_FinancialInstrumentAxis_91d586fa-1a6c-4fe1-a6eb-cc79da42aafb" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_91d586fa-1a6c-4fe1-a6eb-cc79da42aafb_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_91d586fa-1a6c-4fe1-a6eb-cc79da42aafb" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_91d586fa-1a6c-4fe1-a6eb-cc79da42aafb_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5762d161-45fb-4795-b727-1bac9dc98f35" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_91d586fa-1a6c-4fe1-a6eb-cc79da42aafb" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5762d161-45fb-4795-b727-1bac9dc98f35" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_e383e31a-b684-4496-921b-86ef468f720b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5762d161-45fb-4795-b727-1bac9dc98f35" xlink:to="loc_us-gaap_CommonStockMember_e383e31a-b684-4496-921b-86ef468f720b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember_7f7280a8-db86-4a7c-8f79-55ff0d89e9e5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5762d161-45fb-4795-b727-1bac9dc98f35" xlink:to="loc_us-gaap_PreferredStockMember_7f7280a8-db86-4a7c-8f79-55ff0d89e9e5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_9c99e777-f54b-4e21-8aea-3dfaf2616f6e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_b1deeb9f-3524-4f79-bcb5-a4d12a14a735" xlink:to="loc_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_9c99e777-f54b-4e21-8aea-3dfaf2616f6e" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofEquityMethodInvestmentsDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofEquityMethodInvestmentsDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofEquityMethodInvestmentsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_3c405add-5a8b-4747-9df9-305c796bdf8c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_0bfc1e29-e66a-4e34-9005-4aa0267287a3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_3c405add-5a8b-4747-9df9-305c796bdf8c" xlink:to="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_0bfc1e29-e66a-4e34-9005-4aa0267287a3" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis_40da7167-eaab-4eab-9318-fd4789575566" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_0bfc1e29-e66a-4e34-9005-4aa0267287a3" xlink:to="loc_us-gaap_InvestmentTypeAxis_40da7167-eaab-4eab-9318-fd4789575566" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_40da7167-eaab-4eab-9318-fd4789575566_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_InvestmentTypeAxis_40da7167-eaab-4eab-9318-fd4789575566" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_40da7167-eaab-4eab-9318-fd4789575566_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_8bdeff32-50a4-4d0f-86c2-c34c0c661d02" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_InvestmentTypeAxis_40da7167-eaab-4eab-9318-fd4789575566" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_8bdeff32-50a4-4d0f-86c2-c34c0c661d02" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealEstateInvestmentsAtEquityMethodMember_debebf13-4cdf-48bb-a06c-0f911061350a" xlink:href="kg-20250930.xsd#kg_RealEstateInvestmentsAtEquityMethodMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_8bdeff32-50a4-4d0f-86c2-c34c0c661d02" xlink:to="loc_kg_RealEstateInvestmentsAtEquityMethodMember_debebf13-4cdf-48bb-a06c-0f911061350a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealEstateInvestmentsAtFairValueMember_154ff99f-b40b-4488-87a9-6d96979430e3" xlink:href="kg-20250930.xsd#kg_RealEstateInvestmentsAtFairValueMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_8bdeff32-50a4-4d0f-86c2-c34c0c661d02" xlink:to="loc_kg_RealEstateInvestmentsAtFairValueMember_154ff99f-b40b-4488-87a9-6d96979430e3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestmentsMember_d1ee7073-a03a-496b-95e6-4aedf47d5628" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_8bdeff32-50a4-4d0f-86c2-c34c0c661d02" xlink:to="loc_us-gaap_OtherInvestmentsMember_d1ee7073-a03a-496b-95e6-4aedf47d5628" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsFairValueOptionMember_68956f1a-017e-4cf1-b6a2-6a443478a9cd" xlink:href="kg-20250930.xsd#kg_InvestmentsFairValueOptionMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_8bdeff32-50a4-4d0f-86c2-c34c0c661d02" xlink:to="loc_kg_InvestmentsFairValueOptionMember_68956f1a-017e-4cf1-b6a2-6a443478a9cd" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments_9fd27ad8-027d-46a9-b6f9-8f517259f0bc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_3c405add-5a8b-4747-9df9-305c796bdf8c" xlink:to="loc_us-gaap_EquityMethodInvestments_9fd27ad8-027d-46a9-b6f9-8f517259f0bc" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsPercentOfTotal_6483c90b-dc5d-4dad-a696-a8dfba546241" xlink:href="kg-20250930.xsd#kg_EquityMethodInvestmentsPercentOfTotal"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_3c405add-5a8b-4747-9df9-305c796bdf8c" xlink:to="loc_kg_EquityMethodInvestmentsPercentOfTotal_6483c90b-dc5d-4dad-a696-a8dfba546241" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofCarryingValueandBeneficialOwnershipPercentageofEquityMethodInvestmentsDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofCarryingValueandBeneficialOwnershipPercentageofEquityMethodInvestmentsDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofCarryingValueandBeneficialOwnershipPercentageofEquityMethodInvestmentsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_7abc64c5-039c-4197-b87c-392568ed31c0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_68e34b9d-9a9a-4609-962b-174eae73ce7e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_7abc64c5-039c-4197-b87c-392568ed31c0" xlink:to="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_68e34b9d-9a9a-4609-962b-174eae73ce7e" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_5cf4b18b-db51-4c85-bc47-d480cc210ecf" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_68e34b9d-9a9a-4609-962b-174eae73ce7e" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_5cf4b18b-db51-4c85-bc47-d480cc210ecf" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_5cf4b18b-db51-4c85-bc47-d480cc210ecf_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_5cf4b18b-db51-4c85-bc47-d480cc210ecf" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_5cf4b18b-db51-4c85-bc47-d480cc210ecf_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_2bcf8a3f-450e-4061-9ccd-b8baff540d69" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_5cf4b18b-db51-4c85-bc47-d480cc210ecf" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_2bcf8a3f-450e-4061-9ccd-b8baff540d69" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVenture1Member_033786c9-a3a6-4258-8db8-bb11e4075ecf" xlink:href="kg-20250930.xsd#kg_SilverstoneVenture1Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_2bcf8a3f-450e-4061-9ccd-b8baff540d69" xlink:to="loc_kg_SilverstoneVenture1Member_033786c9-a3a6-4258-8db8-bb11e4075ecf" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVenture2Member_9daff5af-e490-423c-a00a-83318bbd1858" xlink:href="kg-20250930.xsd#kg_SilverstoneVenture2Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_2bcf8a3f-450e-4061-9ccd-b8baff540d69" xlink:to="loc_kg_SilverstoneVenture2Member_9daff5af-e490-423c-a00a-83318bbd1858" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVenture3Member_cfcbf5d9-d929-405c-bec6-e955e68f3b90" xlink:href="kg-20250930.xsd#kg_SilverstoneVenture3Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_2bcf8a3f-450e-4061-9ccd-b8baff540d69" xlink:to="loc_kg_SilverstoneVenture3Member_cfcbf5d9-d929-405c-bec6-e955e68f3b90" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ExtellHudsonWaterfrontHoldingsMember_4c195279-bb79-46d0-a114-aec6f3013c20" xlink:href="kg-20250930.xsd#kg_ExtellHudsonWaterfrontHoldingsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_2bcf8a3f-450e-4061-9ccd-b8baff540d69" xlink:to="loc_kg_ExtellHudsonWaterfrontHoldingsMember_4c195279-bb79-46d0-a114-aec6f3013c20" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeidenLPSeidenMGMTLPMember_5a6a2b3d-331e-4b81-8f29-a0929423cfff" xlink:href="kg-20250930.xsd#kg_SeidenLPSeidenMGMTLPMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_2bcf8a3f-450e-4061-9ccd-b8baff540d69" xlink:to="loc_kg_SeidenLPSeidenMGMTLPMember_5a6a2b3d-331e-4b81-8f29-a0929423cfff" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments_0a56b0ae-7405-4d44-88f8-d1a901550674" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_7abc64c5-039c-4197-b87c-392568ed31c0" xlink:to="loc_us-gaap_EquityMethodInvestments_0a56b0ae-7405-4d44-88f8-d1a901550674" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage_e3026fe5-b5de-4af6-80ba-02a19ca06550" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_7abc64c5-039c-4197-b87c-392568ed31c0" xlink:to="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage_e3026fe5-b5de-4af6-80ba-02a19ca06550" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsInvesteeRevenue_ab2eb092-c366-45f8-824f-2c0f5f289f19" xlink:href="kg-20250930.xsd#kg_EquityMethodInvestmentsInvesteeRevenue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_7abc64c5-039c-4197-b87c-392568ed31c0" xlink:to="loc_kg_EquityMethodInvestmentsInvesteeRevenue_ab2eb092-c366-45f8-824f-2c0f5f289f19" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments_209a22eb-438b-449d-b8b5-d8400a94a181" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_7abc64c5-039c-4197-b87c-392568ed31c0" xlink:to="loc_us-gaap_IncomeLossFromEquityMethodInvestments_209a22eb-438b-449d-b8b5-d8400a94a181" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GainLossOnEquityMethodInvestments_8435aa83-19ab-45f2-b011-e6169cac40eb" xlink:href="kg-20250930.xsd#kg_GainLossOnEquityMethodInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_7abc64c5-039c-4197-b87c-392568ed31c0" xlink:to="loc_kg_GainLossOnEquityMethodInvestments_8435aa83-19ab-45f2-b011-e6169cac40eb" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofNetInvestmentIncomeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofNetInvestmentIncomeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofNetInvestmentIncomeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsLineItems_f8266f90-f2d9-4bd5-8bfd-c82b205f0f95" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsTable_c740562b-2e48-4571-af92-e7ea5240bb6e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_f8266f90-f2d9-4bd5-8bfd-c82b205f0f95" xlink:to="loc_us-gaap_ScheduleOfInvestmentsTable_c740562b-2e48-4571-af92-e7ea5240bb6e" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis_2b21bdd4-e569-4d37-9464-346bcef99dfa" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentsTable_c740562b-2e48-4571-af92-e7ea5240bb6e" xlink:to="loc_us-gaap_InvestmentTypeAxis_2b21bdd4-e569-4d37-9464-346bcef99dfa" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_2b21bdd4-e569-4d37-9464-346bcef99dfa_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_InvestmentTypeAxis_2b21bdd4-e569-4d37-9464-346bcef99dfa" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_2b21bdd4-e569-4d37-9464-346bcef99dfa_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_ba1a6db0-4ad7-4345-b6d8-205db72d36b1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_InvestmentTypeAxis_2b21bdd4-e569-4d37-9464-346bcef99dfa" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_ba1a6db0-4ad7-4345-b6d8-205db72d36b1" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedIncomeSecuritiesMember_3c759106-27a5-4ea0-8f1b-9064ce6a43c9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FixedIncomeSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_ba1a6db0-4ad7-4345-b6d8-205db72d36b1" xlink:to="loc_us-gaap_FixedIncomeSecuritiesMember_3c759106-27a5-4ea0-8f1b-9064ce6a43c9" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FundsWithheldArrangementMember_c6656f54-96f8-4a94-8975-6bf3a40b0651" xlink:href="kg-20250930.xsd#kg_FundsWithheldArrangementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_ba1a6db0-4ad7-4345-b6d8-205db72d36b1" xlink:to="loc_kg_FundsWithheldArrangementMember_c6656f54-96f8-4a94-8975-6bf3a40b0651" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NotesReceivableRelatedPartyMember_82bb9d01-63f6-4f3e-8b3a-a38a4811d0b9" xlink:href="kg-20250930.xsd#kg_NotesReceivableRelatedPartyMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_ba1a6db0-4ad7-4345-b6d8-205db72d36b1" xlink:to="loc_kg_NotesReceivableRelatedPartyMember_82bb9d01-63f6-4f3e-8b3a-a38a4811d0b9" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentMember_81ca384f-6e77-4121-8668-ec7670dc90ca" xlink:href="kg-20250930.xsd#kg_OtherInvestmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_ba1a6db0-4ad7-4345-b6d8-205db72d36b1" xlink:to="loc_kg_OtherInvestmentMember_81ca384f-6e77-4121-8668-ec7670dc90ca" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CashAndCashEquivalentsAndOtherMember_429832be-d2c3-49d5-93e2-5fdcc6408640" xlink:href="kg-20250930.xsd#kg_CashAndCashEquivalentsAndOtherMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_ba1a6db0-4ad7-4345-b6d8-205db72d36b1" xlink:to="loc_kg_CashAndCashEquivalentsAndOtherMember_429832be-d2c3-49d5-93e2-5fdcc6408640" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterestAndDividend_1c982494-ae3c-456c-bbf5-8e4134f60c6b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInterestAndDividend"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_f8266f90-f2d9-4bd5-8bfd-c82b205f0f95" xlink:to="loc_us-gaap_InvestmentIncomeInterestAndDividend_1c982494-ae3c-456c-bbf5-8e4134f60c6b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInvestmentExpense_af43ec9d-af02-4c5c-95fb-805033a264a4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInvestmentExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_f8266f90-f2d9-4bd5-8bfd-c82b205f0f95" xlink:to="loc_us-gaap_InvestmentIncomeInvestmentExpense_af43ec9d-af02-4c5c-95fb-805033a264a4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeNet_9557b164-477f-4108-8285-3dc8fb0f4ce8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems_f8266f90-f2d9-4bd5-8bfd-c82b205f0f95" xlink:to="loc_us-gaap_InvestmentIncomeNet_9557b164-477f-4108-8285-3dc8fb0f4ce8" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofNetRealizedandUnrealizedInvestmentGainsLossesDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofNetRealizedandUnrealizedInvestmentGainsLossesDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofNetRealizedandUnrealizedInvestmentGainsLossesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGainLossOnInvestmentsTable_7fb27cef-8ba6-442d-a3b0-955df5bf6857" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGainLossOnInvestmentsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_us-gaap_ScheduleOfGainLossOnInvestmentsTable_7fb27cef-8ba6-442d-a3b0-955df5bf6857" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_d8225a4c-397b-416c-8a3b-771bc77aaa50" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsTable_7fb27cef-8ba6-442d-a3b0-955df5bf6857" xlink:to="loc_us-gaap_FinancialInstrumentAxis_d8225a4c-397b-416c-8a3b-771bc77aaa50" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_d8225a4c-397b-416c-8a3b-771bc77aaa50_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_d8225a4c-397b-416c-8a3b-771bc77aaa50" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_d8225a4c-397b-416c-8a3b-771bc77aaa50_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_9f5bd1cb-588a-4289-9f5c-36ba11e62bb7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_d8225a4c-397b-416c-8a3b-771bc77aaa50" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_9f5bd1cb-588a-4289-9f5c-36ba11e62bb7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember_1186dcff-ad60-4bd6-ba24-a60643a6bd17" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_9f5bd1cb-588a-4289-9f5c-36ba11e62bb7" xlink:to="loc_us-gaap_FixedMaturitiesMember_1186dcff-ad60-4bd6-ba24-a60643a6bd17" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherDebtSecuritiesMember_bca2ac3a-0604-423a-9282-207543ad66a4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherDebtSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_9f5bd1cb-588a-4289-9f5c-36ba11e62bb7" xlink:to="loc_us-gaap_OtherDebtSecuritiesMember_bca2ac3a-0604-423a-9282-207543ad66a4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain_21dd7f55-16e5-4a46-a8bb-2399aded32b0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain_21dd7f55-16e5-4a46-a8bb-2399aded32b0" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_167c9259-4a52-43db-8144-d0ca6551c729" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_167c9259-4a52-43db-8144-d0ca6551c729" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_a5eb9cb8-8446-4280-bbc1-e8f4cfe95145" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_a5eb9cb8-8446-4280-bbc1-e8f4cfe95145" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain_37753b25-b452-45e0-a9f7-9273caf84593" xlink:href="kg-20250930.xsd#kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain_37753b25-b452-45e0-a9f7-9273caf84593" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss_95f04683-b0f1-4fcf-9776-26314ae3cafc" xlink:href="kg-20250930.xsd#kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss_95f04683-b0f1-4fcf-9776-26314ae3cafc" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiGainLoss_0ed46b5f-60bb-4156-a858-75b1af84fb72" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiGainLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_us-gaap_EquitySecuritiesFvNiGainLoss_0ed46b5f-60bb-4156-a858-75b1af84fb72" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MarketableSecuritiesRealizedGain_29a53364-31f1-49ad-a4a8-52664a700628" xlink:href="kg-20250930.xsd#kg_MarketableSecuritiesRealizedGain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_kg_MarketableSecuritiesRealizedGain_29a53364-31f1-49ad-a4a8-52664a700628" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MarketableSecuritiesRealizedLoss_2cbe3fcb-9598-467e-80f6-0fa441b5f4fd" xlink:href="kg-20250930.xsd#kg_MarketableSecuritiesRealizedLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_kg_MarketableSecuritiesRealizedLoss_2cbe3fcb-9598-467e-80f6-0fa441b5f4fd" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities_a76d7376-fa8c-4181-98dd-00b3a70c06e5" xlink:href="kg-20250930.xsd#kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities_a76d7376-fa8c-4181-98dd-00b3a70c06e5" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealizedAndUnrealizedGainOnInvestments_1e545df8-9ed2-4351-bd58-3cb97b375f13" xlink:href="kg-20250930.xsd#kg_RealizedAndUnrealizedGainOnInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_kg_RealizedAndUnrealizedGainOnInvestments_1e545df8-9ed2-4351-bd58-3cb97b375f13" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealizedAndUnrealizedLossOnInvestments_bb77d0bf-9e40-462b-b30a-13db79acc14a" xlink:href="kg-20250930.xsd#kg_RealizedAndUnrealizedLossOnInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_kg_RealizedAndUnrealizedLossOnInvestments_bb77d0bf-9e40-462b-b30a-13db79acc14a" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestments_27312235-0515-4cd9-9835-c7dda211f81b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_us-gaap_GainLossOnInvestments_27312235-0515-4cd9-9835-c7dda211f81b" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiGainLoss_3f3ad6ee-2867-4ee5-9d82-beaca2f94e33" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiGainLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiRealizedGainLoss_31051b4a-9b8e-4e3a-b5c4-d6631eb7c52c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiRealizedGainLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_us-gaap_EquitySecuritiesFvNiRealizedGainLoss_31051b4a-9b8e-4e3a-b5c4-d6631eb7c52c" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss_2315af81-12b5-455c-8360-3ab83618523d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_4862dbb1-24cd-4990-8c56-fca755308351" xlink:to="loc_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss_2315af81-12b5-455c-8360-3ab83618523d" xlink:type="arc" order="14"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/InvestmentsScheduleofFairValueofRestrictedAssetsDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#InvestmentsScheduleofFairValueofRestrictedAssetsDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/InvestmentsScheduleofFairValueofRestrictedAssetsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsLineItems_b552c690-9e3f-4c77-8346-a9812ad3765f" xlink:href="kg-20250930.xsd#kg_RestrictedCashAndInvestmentsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleOfRestrictedCashAndInvestmentsTable_a122be1b-3885-48ff-818b-04a36f52668a" xlink:href="kg-20250930.xsd#kg_ScheduleOfRestrictedCashAndInvestmentsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_kg_RestrictedCashAndInvestmentsLineItems_b552c690-9e3f-4c77-8346-a9812ad3765f" xlink:to="loc_kg_ScheduleOfRestrictedCashAndInvestmentsTable_a122be1b-3885-48ff-818b-04a36f52668a" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsTypeAxis_0850252f-1488-46a6-9ab8-98d3110558e8" xlink:href="kg-20250930.xsd#kg_RestrictedCashAndInvestmentsTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_kg_ScheduleOfRestrictedCashAndInvestmentsTable_a122be1b-3885-48ff-818b-04a36f52668a" xlink:to="loc_kg_RestrictedCashAndInvestmentsTypeAxis_0850252f-1488-46a6-9ab8-98d3110558e8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsTypeDomain_0850252f-1488-46a6-9ab8-98d3110558e8_default" xlink:href="kg-20250930.xsd#kg_RestrictedCashAndInvestmentsTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_kg_RestrictedCashAndInvestmentsTypeAxis_0850252f-1488-46a6-9ab8-98d3110558e8" xlink:to="loc_kg_RestrictedCashAndInvestmentsTypeDomain_0850252f-1488-46a6-9ab8-98d3110558e8_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsTypeDomain_4bde08d5-a006-43b9-8e58-3d0fc9d71fb9" xlink:href="kg-20250930.xsd#kg_RestrictedCashAndInvestmentsTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_kg_RestrictedCashAndInvestmentsTypeAxis_0850252f-1488-46a6-9ab8-98d3110558e8" xlink:to="loc_kg_RestrictedCashAndInvestmentsTypeDomain_4bde08d5-a006-43b9-8e58-3d0fc9d71fb9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ThirdPartyAgreementsMember_83a84f42-d07b-4b14-9f65-5f686e6226f0" xlink:href="kg-20250930.xsd#kg_ThirdPartyAgreementsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RestrictedCashAndInvestmentsTypeDomain_4bde08d5-a006-43b9-8e58-3d0fc9d71fb9" xlink:to="loc_kg_ThirdPartyAgreementsMember_83a84f42-d07b-4b14-9f65-5f686e6226f0" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyAgreementsMember_c7321beb-fbf1-4e1b-80a9-672c26a95f57" xlink:href="kg-20250930.xsd#kg_RelatedPartyAgreementsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RestrictedCashAndInvestmentsTypeDomain_4bde08d5-a006-43b9-8e58-3d0fc9d71fb9" xlink:to="loc_kg_RelatedPartyAgreementsMember_c7321beb-fbf1-4e1b-80a9-672c26a95f57" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalents_d944145a-24bd-457b-8aed-1411769deaf4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndCashEquivalents"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RestrictedCashAndInvestmentsLineItems_b552c690-9e3f-4c77-8346-a9812ad3765f" xlink:to="loc_us-gaap_RestrictedCashAndCashEquivalents_d944145a-24bd-457b-8aed-1411769deaf4" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedInvestments_241c8070-7f7e-4eef-9384-b5ae36859a68" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RestrictedCashAndInvestmentsLineItems_b552c690-9e3f-4c77-8346-a9812ad3765f" xlink:to="loc_us-gaap_RestrictedInvestments_241c8070-7f7e-4eef-9384-b5ae36859a68" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedInvestmentLiability_fe363fc0-193a-49c8-8cbd-2afa5b15ccc4" xlink:href="kg-20250930.xsd#kg_RestrictedInvestmentLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RestrictedCashAndInvestmentsLineItems_b552c690-9e3f-4c77-8346-a9812ad3765f" xlink:to="loc_kg_RestrictedInvestmentLiability_fe363fc0-193a-49c8-8cbd-2afa5b15ccc4" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedInvestmentNetOfLiabilities_5102bb5a-6d1e-4429-b58d-23ba8286240e" xlink:href="kg-20250930.xsd#kg_RestrictedInvestmentNetOfLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RestrictedCashAndInvestmentsLineItems_b552c690-9e3f-4c77-8346-a9812ad3765f" xlink:to="loc_kg_RestrictedInvestmentNetOfLiabilities_5102bb5a-6d1e-4429-b58d-23ba8286240e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndInvestments_a41761be-3751-4aad-9239-930595932ef7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RestrictedCashAndInvestmentsLineItems_b552c690-9e3f-4c77-8346-a9812ad3765f" xlink:to="loc_us-gaap_RestrictedCashAndInvestments_a41761be-3751-4aad-9239-930595932ef7" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsOriginalOrAmortizedCostBasis_30b2cf88-d9d7-40d9-9579-00cd94419e27" xlink:href="kg-20250930.xsd#kg_InvestmentsOriginalOrAmortizedCostBasis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RestrictedCashAndInvestmentsLineItems_b552c690-9e3f-4c77-8346-a9812ad3765f" xlink:to="loc_kg_InvestmentsOriginalOrAmortizedCostBasis_30b2cf88-d9d7-40d9-9579-00cd94419e27" xlink:type="arc" order="5"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/FairValueofFinancialInstrumentsScheduleofFinancialInstrumentsMeasuredatFairValueonaRecurringBasisDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#FairValueofFinancialInstrumentsScheduleofFinancialInstrumentsMeasuredatFairValueonaRecurringBasisDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/FairValueofFinancialInstrumentsScheduleofFinancialInstrumentsMeasuredatFairValueonaRecurringBasisDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_e0b8c07e-4873-4ba1-8d9d-895e3c54e01d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_d9ab49ea-bfec-41a1-9215-59d060db6f62" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_e0b8c07e-4873-4ba1-8d9d-895e3c54e01d" xlink:to="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_d9ab49ea-bfec-41a1-9215-59d060db6f62" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis_d93dc48f-8ccb-4b44-a7a6-c2069b114e07" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_d9ab49ea-bfec-41a1-9215-59d060db6f62" xlink:to="loc_us-gaap_FairValueByMeasurementFrequencyAxis_d93dc48f-8ccb-4b44-a7a6-c2069b114e07" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain_d93dc48f-8ccb-4b44-a7a6-c2069b114e07_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis_d93dc48f-8ccb-4b44-a7a6-c2069b114e07" xlink:to="loc_us-gaap_FairValueMeasurementFrequencyDomain_d93dc48f-8ccb-4b44-a7a6-c2069b114e07_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain_5213e5ff-80e0-4d9d-9a8f-59e4697f33e1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis_d93dc48f-8ccb-4b44-a7a6-c2069b114e07" xlink:to="loc_us-gaap_FairValueMeasurementFrequencyDomain_5213e5ff-80e0-4d9d-9a8f-59e4697f33e1" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember_f6a55874-b100-4de0-8a4b-b59b9f2e2b64" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain_5213e5ff-80e0-4d9d-9a8f-59e4697f33e1" xlink:to="loc_us-gaap_FairValueMeasurementsRecurringMember_f6a55874-b100-4de0-8a4b-b59b9f2e2b64" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_58051631-afb7-4d8e-94e7-a8639d769bd8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_d9ab49ea-bfec-41a1-9215-59d060db6f62" xlink:to="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_58051631-afb7-4d8e-94e7-a8639d769bd8" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_58051631-afb7-4d8e-94e7-a8639d769bd8_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_58051631-afb7-4d8e-94e7-a8639d769bd8" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_58051631-afb7-4d8e-94e7-a8639d769bd8_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_b60ba3fc-1557-4a0a-8de0-66475cfd7793" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_58051631-afb7-4d8e-94e7-a8639d769bd8" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_b60ba3fc-1557-4a0a-8de0-66475cfd7793" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member_7d74a290-6a24-474c-ad97-bf974d77dedf" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_b60ba3fc-1557-4a0a-8de0-66475cfd7793" xlink:to="loc_us-gaap_FairValueInputsLevel1Member_7d74a290-6a24-474c-ad97-bf974d77dedf" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member_6404d97c-666d-4064-9f24-e00a52be8b1a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_b60ba3fc-1557-4a0a-8de0-66475cfd7793" xlink:to="loc_us-gaap_FairValueInputsLevel2Member_6404d97c-666d-4064-9f24-e00a52be8b1a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member_484585b0-caaf-4887-ba81-ab254879df19" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_b60ba3fc-1557-4a0a-8de0-66475cfd7793" xlink:to="loc_us-gaap_FairValueInputsLevel3Member_484585b0-caaf-4887-ba81-ab254879df19" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_3e946339-19a3-4f71-ac21-327a4121b508" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_b60ba3fc-1557-4a0a-8de0-66475cfd7793" xlink:to="loc_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_3e946339-19a3-4f71-ac21-327a4121b508" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_a6efab71-c1a1-47b7-be49-4ffbb101b57a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_d9ab49ea-bfec-41a1-9215-59d060db6f62" xlink:to="loc_us-gaap_FinancialInstrumentAxis_a6efab71-c1a1-47b7-be49-4ffbb101b57a" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_a6efab71-c1a1-47b7-be49-4ffbb101b57a_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_a6efab71-c1a1-47b7-be49-4ffbb101b57a" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_a6efab71-c1a1-47b7-be49-4ffbb101b57a_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_2138a37a-f7e1-4166-bba1-c48e67f75643" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_a6efab71-c1a1-47b7-be49-4ffbb101b57a" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_2138a37a-f7e1-4166-bba1-c48e67f75643" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryBondSecuritiesMember_1f077d92-6164-4010-9bc6-b9620ece3f81" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USTreasuryBondSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_2138a37a-f7e1-4166-bba1-c48e67f75643" xlink:to="loc_us-gaap_USTreasuryBondSecuritiesMember_1f077d92-6164-4010-9bc6-b9620ece3f81" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_e2d5ccbb-7497-440c-9648-e693d9130730" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_2138a37a-f7e1-4166-bba1-c48e67f75643" xlink:to="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_e2d5ccbb-7497-440c-9648-e693d9130730" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignGovernmentDebtMember_5afb822b-e8e1-4dfd-bd01-edf94db39ec6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignGovernmentDebtMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_2138a37a-f7e1-4166-bba1-c48e67f75643" xlink:to="loc_us-gaap_ForeignGovernmentDebtMember_5afb822b-e8e1-4dfd-bd01-edf94db39ec6" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralizedLoanObligationsMember_90e96649-2601-4dc4-88cf-d4ce74765321" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CollateralizedLoanObligationsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_2138a37a-f7e1-4166-bba1-c48e67f75643" xlink:to="loc_us-gaap_CollateralizedLoanObligationsMember_90e96649-2601-4dc4-88cf-d4ce74765321" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateBondSecuritiesMember_4bdb84b5-7c37-450c-aabf-5808d2819ebd" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateBondSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_2138a37a-f7e1-4166-bba1-c48e67f75643" xlink:to="loc_us-gaap_CorporateBondSecuritiesMember_4bdb84b5-7c37-450c-aabf-5808d2819ebd" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities_e04dc747-ed60-4768-a8ef-1ba23f899c5a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_e0b8c07e-4873-4ba1-8d9d-895e3c54e01d" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities_e04dc747-ed60-4768-a8ef-1ba23f899c5a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNi_32eff3c2-dd08-4016-9876-59c0a8deb634" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNi"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_e0b8c07e-4873-4ba1-8d9d-895e3c54e01d" xlink:to="loc_us-gaap_EquitySecuritiesFvNi_32eff3c2-dd08-4016-9876-59c0a8deb634" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestment_6a57c16a-f0ca-4128-a834-dd2938f65785" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AlternativeInvestment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_e0b8c07e-4873-4ba1-8d9d-895e3c54e01d" xlink:to="loc_us-gaap_AlternativeInvestment_6a57c16a-f0ca-4128-a834-dd2938f65785" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure_79f90838-7fe6-4be2-a5c2-217a561fa2b3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_e0b8c07e-4873-4ba1-8d9d-895e3c54e01d" xlink:to="loc_us-gaap_AssetsFairValueDisclosure_79f90838-7fe6-4be2-a5c2-217a561fa2b3" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets_bb678897-ddeb-4e41-86d7-bafc03647452" xlink:href="kg-20250930.xsd#kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_e0b8c07e-4873-4ba1-8d9d-895e3c54e01d" xlink:to="loc_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets_bb678897-ddeb-4e41-86d7-bafc03647452" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities_953f2f48-7413-4a8f-82ed-645e190e31c5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_e0b8c07e-4873-4ba1-8d9d-895e3c54e01d" xlink:to="loc_us-gaap_DerivativeLiabilities_953f2f48-7413-4a8f-82ed-645e190e31c5" xlink:type="arc" order="5"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/FairValueofFinancialInstrumentsNarrativeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#FairValueofFinancialInstrumentsNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/FairValueofFinancialInstrumentsNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_897e9af4-676f-4133-8a36-fd8a8c497bd1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_3f672aa6-bde7-4b3d-b7dd-0ff254638497" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_897e9af4-676f-4133-8a36-fd8a8c497bd1" xlink:to="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_3f672aa6-bde7-4b3d-b7dd-0ff254638497" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis_426e3fcc-acf4-499f-b363-74882535250d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_3f672aa6-bde7-4b3d-b7dd-0ff254638497" xlink:to="loc_us-gaap_FairValueByMeasurementBasisAxis_426e3fcc-acf4-499f-b363-74882535250d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_426e3fcc-acf4-499f-b363-74882535250d_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis_426e3fcc-acf4-499f-b363-74882535250d" xlink:to="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_426e3fcc-acf4-499f-b363-74882535250d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain_270ea63d-a8b4-4cb0-9999-ac0af32843bc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis_426e3fcc-acf4-499f-b363-74882535250d" xlink:to="loc_us-gaap_FairValueDisclosureItemAmountsDomain_270ea63d-a8b4-4cb0-9999-ac0af32843bc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_33ebc20a-7fe5-4973-bb28-e79c922184ab" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain_270ea63d-a8b4-4cb0-9999-ac0af32843bc" xlink:to="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_33ebc20a-7fe5-4973-bb28-e79c922184ab" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember_689ff599-d0d1-4089-a296-0631e683bceb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_33ebc20a-7fe5-4973-bb28-e79c922184ab" xlink:to="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember_689ff599-d0d1-4089-a296-0631e683bceb" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis_afe11b92-574f-4b01-9438-61d8de95dfa6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_3f672aa6-bde7-4b3d-b7dd-0ff254638497" xlink:to="loc_us-gaap_FairValueByMeasurementFrequencyAxis_afe11b92-574f-4b01-9438-61d8de95dfa6" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain_afe11b92-574f-4b01-9438-61d8de95dfa6_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis_afe11b92-574f-4b01-9438-61d8de95dfa6" xlink:to="loc_us-gaap_FairValueMeasurementFrequencyDomain_afe11b92-574f-4b01-9438-61d8de95dfa6_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain_d65d104b-a788-4719-9bea-3f63a6e65f8c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis_afe11b92-574f-4b01-9438-61d8de95dfa6" xlink:to="loc_us-gaap_FairValueMeasurementFrequencyDomain_d65d104b-a788-4719-9bea-3f63a6e65f8c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember_4b92335b-3401-473a-91d5-4e6e5ce6c053" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain_d65d104b-a788-4719-9bea-3f63a6e65f8c" xlink:to="loc_us-gaap_FairValueMeasurementsRecurringMember_4b92335b-3401-473a-91d5-4e6e5ce6c053" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_a2e2e1c9-03d6-4b9e-92aa-c7fc4cbf2889" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_3f672aa6-bde7-4b3d-b7dd-0ff254638497" xlink:to="loc_us-gaap_FinancialInstrumentAxis_a2e2e1c9-03d6-4b9e-92aa-c7fc4cbf2889" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_a2e2e1c9-03d6-4b9e-92aa-c7fc4cbf2889_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_a2e2e1c9-03d6-4b9e-92aa-c7fc4cbf2889" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_a2e2e1c9-03d6-4b9e-92aa-c7fc4cbf2889_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_b5c03bee-c193-4389-9864-de8464a1cdc4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_a2e2e1c9-03d6-4b9e-92aa-c7fc4cbf2889" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_b5c03bee-c193-4389-9864-de8464a1cdc4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember_e55ad86b-f1d7-49a9-a475-2d97cff56ef3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_b5c03bee-c193-4389-9864-de8464a1cdc4" xlink:to="loc_us-gaap_FixedMaturitiesMember_e55ad86b-f1d7-49a9-a475-2d97cff56ef3" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_3c27c4e5-5036-4d3d-aa43-808cc2888cc0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_3f672aa6-bde7-4b3d-b7dd-0ff254638497" xlink:to="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_3c27c4e5-5036-4d3d-aa43-808cc2888cc0" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_3c27c4e5-5036-4d3d-aa43-808cc2888cc0_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_3c27c4e5-5036-4d3d-aa43-808cc2888cc0" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_3c27c4e5-5036-4d3d-aa43-808cc2888cc0_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_56529097-eba8-4bb9-a450-810db622bc80" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_3c27c4e5-5036-4d3d-aa43-808cc2888cc0" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_56529097-eba8-4bb9-a450-810db622bc80" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member_50f59e7c-624c-4123-a81b-31f9dbd58e4f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_56529097-eba8-4bb9-a450-810db622bc80" xlink:to="loc_us-gaap_FairValueInputsLevel3Member_50f59e7c-624c-4123-a81b-31f9dbd58e4f" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis_55da5c88-9e15-4bae-acbb-e8b50255e433" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_3f672aa6-bde7-4b3d-b7dd-0ff254638497" xlink:to="loc_us-gaap_ValuationTechniqueAxis_55da5c88-9e15-4bae-acbb-e8b50255e433" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain_55da5c88-9e15-4bae-acbb-e8b50255e433_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ValuationTechniqueAxis_55da5c88-9e15-4bae-acbb-e8b50255e433" xlink:to="loc_us-gaap_ValuationTechniqueDomain_55da5c88-9e15-4bae-acbb-e8b50255e433_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain_315d9105-f4bc-455a-9862-8754cced7cb3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ValuationTechniqueAxis_55da5c88-9e15-4bae-acbb-e8b50255e433" xlink:to="loc_us-gaap_ValuationTechniqueDomain_315d9105-f4bc-455a-9862-8754cced7cb3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember_9eb2c06c-a9f0-42c4-bd1f-d52641c526a0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ValuationTechniqueDomain_315d9105-f4bc-455a-9862-8754cced7cb3" xlink:to="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember_9eb2c06c-a9f0-42c4-bd1f-d52641c526a0" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis_f08e7e67-617d-493e-9140-34490a7053d9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_3f672aa6-bde7-4b3d-b7dd-0ff254638497" xlink:to="loc_us-gaap_InvestmentTypeAxis_f08e7e67-617d-493e-9140-34490a7053d9" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_f08e7e67-617d-493e-9140-34490a7053d9_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_InvestmentTypeAxis_f08e7e67-617d-493e-9140-34490a7053d9" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_f08e7e67-617d-493e-9140-34490a7053d9_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_a25df109-194a-42b1-87c7-151c6e237d3c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_InvestmentTypeAxis_f08e7e67-617d-493e-9140-34490a7053d9" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_a25df109-194a-42b1-87c7-151c6e237d3c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DirectLendingEntitiesMember_2317bf81-9518-4f70-9571-13960def9275" xlink:href="kg-20250930.xsd#kg_DirectLendingEntitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_a25df109-194a-42b1-87c7-151c6e237d3c" xlink:to="loc_kg_DirectLendingEntitiesMember_2317bf81-9518-4f70-9571-13960def9275" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage_12d596f0-87dd-4c63-a978-a58ac3201779" xlink:href="kg-20250930.xsd#kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_897e9af4-676f-4133-8a36-fd8a8c497bd1" xlink:to="loc_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage_12d596f0-87dd-4c63-a978-a58ac3201779" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure_6631b355-2c4e-4195-9f71-dac52f96e6c6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_897e9af4-676f-4133-8a36-fd8a8c497bd1" xlink:to="loc_us-gaap_AssetsFairValueDisclosure_6631b355-2c4e-4195-9f71-dac52f96e6c6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities_91f63c62-bd7a-48f1-99a3-f8ef57a4b32e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_897e9af4-676f-4133-8a36-fd8a8c497bd1" xlink:to="loc_us-gaap_DerivativeLiabilities_91f63c62-bd7a-48f1-99a3-f8ef57a4b32e" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestments_fd94a1c8-ef7d-4796-ba8b-cde3467fee4f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_897e9af4-676f-4133-8a36-fd8a8c497bd1" xlink:to="loc_us-gaap_OtherInvestments_fd94a1c8-ef7d-4796-ba8b-cde3467fee4f" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNi_907d36bf-d700-41c2-aece-d58eed4d09e7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNi"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_897e9af4-676f-4133-8a36-fd8a8c497bd1" xlink:to="loc_us-gaap_EquitySecuritiesFvNi_907d36bf-d700-41c2-aece-d58eed4d09e7" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/FairValueofFinancialInstrumentsScheduleofSignificantUnobservableInputsforDeterminingFairValueofOtherInvestmentsDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#FairValueofFinancialInstrumentsScheduleofSignificantUnobservableInputsforDeterminingFairValueofOtherInvestmentsDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/FairValueofFinancialInstrumentsScheduleofSignificantUnobservableInputsforDeterminingFairValueofOtherInvestmentsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_08c1e866-1937-4856-a0ee-437825f822a7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_ad94190f-e507-48cf-9b30-1014fb11c6ea" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_08c1e866-1937-4856-a0ee-437825f822a7" xlink:to="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_ad94190f-e507-48cf-9b30-1014fb11c6ea" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_b1f08172-409f-454d-aed5-bed533d402a2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_ad94190f-e507-48cf-9b30-1014fb11c6ea" xlink:to="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_b1f08172-409f-454d-aed5-bed533d402a2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_b1f08172-409f-454d-aed5-bed533d402a2_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_b1f08172-409f-454d-aed5-bed533d402a2" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_b1f08172-409f-454d-aed5-bed533d402a2_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_659dd171-5e57-4b04-a66b-396cd673d50c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_b1f08172-409f-454d-aed5-bed533d402a2" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_659dd171-5e57-4b04-a66b-396cd673d50c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member_fc6443a8-388d-4e09-b5a2-894e6ae1d51c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_659dd171-5e57-4b04-a66b-396cd673d50c" xlink:to="loc_us-gaap_FairValueInputsLevel3Member_fc6443a8-388d-4e09-b5a2-894e6ae1d51c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis_04c08caa-4491-4e9e-ac83-61b879e1f63a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_ad94190f-e507-48cf-9b30-1014fb11c6ea" xlink:to="loc_us-gaap_FairValueByMeasurementFrequencyAxis_04c08caa-4491-4e9e-ac83-61b879e1f63a" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain_04c08caa-4491-4e9e-ac83-61b879e1f63a_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis_04c08caa-4491-4e9e-ac83-61b879e1f63a" xlink:to="loc_us-gaap_FairValueMeasurementFrequencyDomain_04c08caa-4491-4e9e-ac83-61b879e1f63a_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain_6ec45bfe-2a33-4a86-950b-d9f7144b5218" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis_04c08caa-4491-4e9e-ac83-61b879e1f63a" xlink:to="loc_us-gaap_FairValueMeasurementFrequencyDomain_6ec45bfe-2a33-4a86-950b-d9f7144b5218" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember_e1e6c426-8beb-4bcc-a82e-ac1bb51d7e98" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain_6ec45bfe-2a33-4a86-950b-d9f7144b5218" xlink:to="loc_us-gaap_FairValueMeasurementsRecurringMember_e1e6c426-8beb-4bcc-a82e-ac1bb51d7e98" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis_f606946a-c265-464e-894d-382ae42a871b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_ad94190f-e507-48cf-9b30-1014fb11c6ea" xlink:to="loc_us-gaap_InvestmentTypeAxis_f606946a-c265-464e-894d-382ae42a871b" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_f606946a-c265-464e-894d-382ae42a871b_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_InvestmentTypeAxis_f606946a-c265-464e-894d-382ae42a871b" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_f606946a-c265-464e-894d-382ae42a871b_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_6fdfd801-8420-4257-812d-a4dfc701e4ff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_InvestmentTypeAxis_f606946a-c265-464e-894d-382ae42a871b" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_6fdfd801-8420-4257-812d-a4dfc701e4ff" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquitySecuritiesInCommonStockMember_dbe031d4-e1d3-4177-a883-6f47c7f1c60e" xlink:href="kg-20250930.xsd#kg_PrivatelyHeldEquitySecuritiesInCommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6fdfd801-8420-4257-812d-a4dfc701e4ff" xlink:to="loc_kg_PrivatelyHeldEquitySecuritiesInCommonStockMember_dbe031d4-e1d3-4177-a883-6f47c7f1c60e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember_e824ce04-56ec-4eb0-8933-2b5d97b5414d" xlink:href="kg-20250930.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6fdfd801-8420-4257-812d-a4dfc701e4ff" xlink:to="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember_e824ce04-56ec-4eb0-8933-2b5d97b5414d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DirectLendingEntitiesMember_62e18205-145c-4081-9af3-f2bb93a7e8bd" xlink:href="kg-20250930.xsd#kg_DirectLendingEntitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6fdfd801-8420-4257-812d-a4dfc701e4ff" xlink:to="loc_kg_DirectLendingEntitiesMember_62e18205-145c-4081-9af3-f2bb93a7e8bd" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsMember_b893c867-7600-4c08-b959-5087accea491" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6fdfd801-8420-4257-812d-a4dfc701e4ff" xlink:to="loc_us-gaap_EquityMethodInvestmentsMember_b893c867-7600-4c08-b959-5087accea491" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_1277d232-b3c5-4036-93f5-71897d9301d4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_ad94190f-e507-48cf-9b30-1014fb11c6ea" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_1277d232-b3c5-4036-93f5-71897d9301d4" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_1277d232-b3c5-4036-93f5-71897d9301d4_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_1277d232-b3c5-4036-93f5-71897d9301d4" xlink:to="loc_us-gaap_EquityComponentDomain_1277d232-b3c5-4036-93f5-71897d9301d4_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_917ff091-f65c-4a47-a9d7-ad103947c715" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_1277d232-b3c5-4036-93f5-71897d9301d4" xlink:to="loc_us-gaap_EquityComponentDomain_917ff091-f65c-4a47-a9d7-ad103947c715" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_46cc0be3-e7cf-46f3-9dd4-aa6586227bc2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_917ff091-f65c-4a47-a9d7-ad103947c715" xlink:to="loc_us-gaap_CommonStockMember_46cc0be3-e7cf-46f3-9dd4-aa6586227bc2" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember_1d745c64-3f41-42d4-a0f3-e000c6ac8259" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_917ff091-f65c-4a47-a9d7-ad103947c715" xlink:to="loc_us-gaap_PreferredStockMember_1d745c64-3f41-42d4-a0f3-e000c6ac8259" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis_069c1cd8-c4fd-4244-92e6-da1a62a9df35" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_ad94190f-e507-48cf-9b30-1014fb11c6ea" xlink:to="loc_us-gaap_ValuationTechniqueAxis_069c1cd8-c4fd-4244-92e6-da1a62a9df35" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain_069c1cd8-c4fd-4244-92e6-da1a62a9df35_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ValuationTechniqueAxis_069c1cd8-c4fd-4244-92e6-da1a62a9df35" xlink:to="loc_us-gaap_ValuationTechniqueDomain_069c1cd8-c4fd-4244-92e6-da1a62a9df35_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain_83dc685d-fc47-45f5-8be0-080f3ac3996e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ValuationTechniqueAxis_069c1cd8-c4fd-4244-92e6-da1a62a9df35" xlink:to="loc_us-gaap_ValuationTechniqueDomain_83dc685d-fc47-45f5-8be0-080f3ac3996e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ValuationTechniqueQuarterlyFinancialStatementsMember_8b1c5b82-c978-4fdd-9192-af75fa054682" xlink:href="kg-20250930.xsd#kg_ValuationTechniqueQuarterlyFinancialStatementsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ValuationTechniqueDomain_83dc685d-fc47-45f5-8be0-080f3ac3996e" xlink:to="loc_kg_ValuationTechniqueQuarterlyFinancialStatementsMember_8b1c5b82-c978-4fdd-9192-af75fa054682" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember_bc8565f3-b641-4ee0-90ec-c5ee946ccdf2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ValuationTechniqueDomain_83dc685d-fc47-45f5-8be0-080f3ac3996e" xlink:to="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember_bc8565f3-b641-4ee0-90ec-c5ee946ccdf2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_7be6190f-92cf-4182-924c-053974feb422" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_ad94190f-e507-48cf-9b30-1014fb11c6ea" xlink:to="loc_srt_RangeAxis_7be6190f-92cf-4182-924c-053974feb422" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_7be6190f-92cf-4182-924c-053974feb422_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_7be6190f-92cf-4182-924c-053974feb422" xlink:to="loc_srt_RangeMember_7be6190f-92cf-4182-924c-053974feb422_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_a9e27fe0-3aed-4a76-9581-926f692856c6" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_7be6190f-92cf-4182-924c-053974feb422" xlink:to="loc_srt_RangeMember_a9e27fe0-3aed-4a76-9581-926f692856c6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember_e0020911-e603-4ece-99f5-26598e9ef528" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_a9e27fe0-3aed-4a76-9581-926f692856c6" xlink:to="loc_srt_MinimumMember_e0020911-e603-4ece-99f5-26598e9ef528" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_d51ba864-2dcd-48f5-9924-7a3ed862d95c" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_a9e27fe0-3aed-4a76-9581-926f692856c6" xlink:to="loc_srt_MaximumMember_d51ba864-2dcd-48f5-9924-7a3ed862d95c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis_129915c1-9149-489b-917c-d73e48d91c04" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_ad94190f-e507-48cf-9b30-1014fb11c6ea" xlink:to="loc_us-gaap_MeasurementInputTypeAxis_129915c1-9149-489b-917c-d73e48d91c04" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain_129915c1-9149-489b-917c-d73e48d91c04_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_MeasurementInputTypeAxis_129915c1-9149-489b-917c-d73e48d91c04" xlink:to="loc_us-gaap_MeasurementInputTypeDomain_129915c1-9149-489b-917c-d73e48d91c04_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain_cb989c66-f349-4ecd-8faa-56d73d68c8b5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_MeasurementInputTypeAxis_129915c1-9149-489b-917c-d73e48d91c04" xlink:to="loc_us-gaap_MeasurementInputTypeDomain_cb989c66-f349-4ecd-8faa-56d73d68c8b5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember_7b680fc8-81c1-4ce5-a22b-c863571b7ef1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_MeasurementInputTypeDomain_cb989c66-f349-4ecd-8faa-56d73d68c8b5" xlink:to="loc_us-gaap_MeasurementInputDiscountRateMember_7b680fc8-81c1-4ce5-a22b-c863571b7ef1" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure_f38c843d-730e-4ba5-8954-a8380c4165c2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_08c1e866-1937-4856-a0ee-437825f822a7" xlink:to="loc_us-gaap_AssetsFairValueDisclosure_f38c843d-730e-4ba5-8954-a8380c4165c2" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities_28774454-5f64-45ec-aadc-a51d6a56a065" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_08c1e866-1937-4856-a0ee-437825f822a7" xlink:to="loc_us-gaap_DerivativeLiabilities_28774454-5f64-45ec-aadc-a51d6a56a065" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityMeasurementInput_d16990e0-cba8-4682-83a5-f8af0668435a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityMeasurementInput"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_08c1e866-1937-4856-a0ee-437825f822a7" xlink:to="loc_us-gaap_DerivativeLiabilityMeasurementInput_d16990e0-cba8-4682-83a5-f8af0668435a" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/FairValueofFinancialInstrumentsScheduleofCarryingValuesandFairValuefortheSeniorNotesDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#FairValueofFinancialInstrumentsScheduleofCarryingValuesandFairValuefortheSeniorNotesDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/FairValueofFinancialInstrumentsScheduleofCarryingValuesandFairValuefortheSeniorNotesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_4f0099de-0635-4f42-bc05-adf4752e3414" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_2660f680-2401-47c7-aa9e-9398040dac68" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_4f0099de-0635-4f42-bc05-adf4752e3414" xlink:to="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_2660f680-2401-47c7-aa9e-9398040dac68" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_1ae4b480-7367-4c8f-9779-706d0565701c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_2660f680-2401-47c7-aa9e-9398040dac68" xlink:to="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_1ae4b480-7367-4c8f-9779-706d0565701c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_1ae4b480-7367-4c8f-9779-706d0565701c_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_1ae4b480-7367-4c8f-9779-706d0565701c" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_1ae4b480-7367-4c8f-9779-706d0565701c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_d1bc769c-bf9c-4854-8345-271a847223e7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_1ae4b480-7367-4c8f-9779-706d0565701c" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_d1bc769c-bf9c-4854-8345-271a847223e7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member_893f6862-b2fc-4ab3-9f86-5cd351867ee0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_d1bc769c-bf9c-4854-8345-271a847223e7" xlink:to="loc_us-gaap_FairValueInputsLevel2Member_893f6862-b2fc-4ab3-9f86-5cd351867ee0" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis_1dfd2bca-77dd-41f7-a1fe-5d684cd9c1fb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_2660f680-2401-47c7-aa9e-9398040dac68" xlink:to="loc_us-gaap_FairValueByMeasurementBasisAxis_1dfd2bca-77dd-41f7-a1fe-5d684cd9c1fb" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_1dfd2bca-77dd-41f7-a1fe-5d684cd9c1fb_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis_1dfd2bca-77dd-41f7-a1fe-5d684cd9c1fb" xlink:to="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_1dfd2bca-77dd-41f7-a1fe-5d684cd9c1fb_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain_a575383d-33f3-4fa0-a757-b4811a6902c2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis_1dfd2bca-77dd-41f7-a1fe-5d684cd9c1fb" xlink:to="loc_us-gaap_FairValueDisclosureItemAmountsDomain_a575383d-33f3-4fa0-a757-b4811a6902c2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_ad1baf2b-67ef-45a3-bc95-f33e64bd722a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain_a575383d-33f3-4fa0-a757-b4811a6902c2" xlink:to="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_ad1baf2b-67ef-45a3-bc95-f33e64bd722a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember_338f63b8-d28f-4911-a3bd-f31730fd88f5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_ad1baf2b-67ef-45a3-bc95-f33e64bd722a" xlink:to="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember_338f63b8-d28f-4911-a3bd-f31730fd88f5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember_8b1ed721-aea8-4ea4-82b6-0252022b12c8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember_ad1baf2b-67ef-45a3-bc95-f33e64bd722a" xlink:to="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember_8b1ed721-aea8-4ea4-82b6-0252022b12c8" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis_bfaa2e9a-fed7-492b-bd8e-afe6eeac105c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_2660f680-2401-47c7-aa9e-9398040dac68" xlink:to="loc_us-gaap_LongtermDebtTypeAxis_bfaa2e9a-fed7-492b-bd8e-afe6eeac105c" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_bfaa2e9a-fed7-492b-bd8e-afe6eeac105c_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_bfaa2e9a-fed7-492b-bd8e-afe6eeac105c" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_bfaa2e9a-fed7-492b-bd8e-afe6eeac105c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_63003070-6c2d-4c12-a4cc-4c6a8c3dcec5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_bfaa2e9a-fed7-492b-bd8e-afe6eeac105c" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_63003070-6c2d-4c12-a4cc-4c6a8c3dcec5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember_4f6012d5-60c1-4d97-89a4-4426e7ceab6b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorNotesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LongtermDebtTypeDomain_63003070-6c2d-4c12-a4cc-4c6a8c3dcec5" xlink:to="loc_us-gaap_SeniorNotesMember_4f6012d5-60c1-4d97-89a4-4426e7ceab6b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis_73d652fe-b587-4212-a426-6402d0e74765" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_2660f680-2401-47c7-aa9e-9398040dac68" xlink:to="loc_us-gaap_DebtInstrumentAxis_73d652fe-b587-4212-a426-6402d0e74765" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_73d652fe-b587-4212-a426-6402d0e74765_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DebtInstrumentAxis_73d652fe-b587-4212-a426-6402d0e74765" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_73d652fe-b587-4212-a426-6402d0e74765_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_90c423e0-9992-4d00-9169-7fb2194d85b8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DebtInstrumentAxis_73d652fe-b587-4212-a426-6402d0e74765" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_90c423e0-9992-4d00-9169-7fb2194d85b8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2016Member_4dbdd7f2-8e10-4621-afae-e7a74c6d4455" xlink:href="kg-20250930.xsd#kg_SeniorNotes2016Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_90c423e0-9992-4d00-9169-7fb2194d85b8" xlink:to="loc_kg_SeniorNotes2016Member_4dbdd7f2-8e10-4621-afae-e7a74c6d4455" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2013Member_2ab9b797-47da-453a-87ca-92921e7c61ac" xlink:href="kg-20250930.xsd#kg_SeniorNotes2013Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_90c423e0-9992-4d00-9169-7fb2194d85b8" xlink:to="loc_kg_SeniorNotes2013Member_2ab9b797-47da-453a-87ca-92921e7c61ac" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_4cf4d3b3-ae07-40ad-a0d6-e3ece5078388" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_4f0099de-0635-4f42-bc05-adf4752e3414" xlink:to="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_4cf4d3b3-ae07-40ad-a0d6-e3ece5078388" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure_0b6569af-56ac-40e2-be90-f48228facef8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosure"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_4f0099de-0635-4f42-bc05-adf4752e3414" xlink:to="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure_0b6569af-56ac-40e2-be90-f48228facef8" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/ShareholdersEquityNarrativeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#ShareholdersEquityNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/ShareholdersEquityNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable_5208e401-7cc9-4b12-9f44-0a8a4d771ddb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_us-gaap_ScheduleOfStockByClassTable_5208e401-7cc9-4b12-9f44-0a8a4d771ddb" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis_364092af-5d4b-4bef-aafb-0f608560c4b9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable_5208e401-7cc9-4b12-9f44-0a8a4d771ddb" xlink:to="loc_us-gaap_BusinessAcquisitionAxis_364092af-5d4b-4bef-aafb-0f608560c4b9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_364092af-5d4b-4bef-aafb-0f608560c4b9_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_364092af-5d4b-4bef-aafb-0f608560c4b9" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_364092af-5d4b-4bef-aafb-0f608560c4b9_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_5df449bf-1015-4d0e-a96c-64235a4fad2b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_364092af-5d4b-4bef-aafb-0f608560c4b9" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_5df449bf-1015-4d0e-a96c-64235a4fad2b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_0bd6ebfd-3f2b-4d57-b373-8b48e7a675f3" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain_5df449bf-1015-4d0e-a96c-64235a4fad2b" xlink:to="loc_kg_KestrelGroupLtd.Member_0bd6ebfd-3f2b-4d57-b373-8b48e7a675f3" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis_5b308592-58a0-4c15-9494-9e564b931aad" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable_5208e401-7cc9-4b12-9f44-0a8a4d771ddb" xlink:to="loc_dei_LegalEntityAxis_5b308592-58a0-4c15-9494-9e564b931aad" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_5b308592-58a0-4c15-9494-9e564b931aad_default" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_dei_LegalEntityAxis_5b308592-58a0-4c15-9494-9e564b931aad" xlink:to="loc_dei_EntityDomain_5b308592-58a0-4c15-9494-9e564b931aad_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_128b0fa8-1a13-4c12-9402-1ff6287840c2" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_dei_LegalEntityAxis_5b308592-58a0-4c15-9494-9e564b931aad" xlink:to="loc_dei_EntityDomain_128b0fa8-1a13-4c12-9402-1ff6287840c2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MaidenReinsuranceMember_6a3b3906-ce6d-4cf2-a599-aff57f4803ea" xlink:href="kg-20250930.xsd#kg_MaidenReinsuranceMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_128b0fa8-1a13-4c12-9402-1ff6287840c2" xlink:to="loc_kg_MaidenReinsuranceMember_6a3b3906-ce6d-4cf2-a599-aff57f4803ea" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameAxis_f57a838a-e5b7-4014-b32d-df52d24936b7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable_5208e401-7cc9-4b12-9f44-0a8a4d771ddb" xlink:to="loc_us-gaap_PlanNameAxis_f57a838a-e5b7-4014-b32d-df52d24936b7" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameDomain_f57a838a-e5b7-4014-b32d-df52d24936b7_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_PlanNameAxis_f57a838a-e5b7-4014-b32d-df52d24936b7" xlink:to="loc_us-gaap_PlanNameDomain_f57a838a-e5b7-4014-b32d-df52d24936b7_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameDomain_ca26f305-c05e-48f1-aea8-c64647f7120d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_PlanNameAxis_f57a838a-e5b7-4014-b32d-df52d24936b7" xlink:to="loc_us-gaap_PlanNameDomain_ca26f305-c05e-48f1-aea8-c64647f7120d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_A2019OmnibusIncentivePlanMember_58d19982-2459-4d96-82d4-a9e09184a3b0" xlink:href="kg-20250930.xsd#kg_A2019OmnibusIncentivePlanMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PlanNameDomain_ca26f305-c05e-48f1-aea8-c64647f7120d" xlink:to="loc_kg_A2019OmnibusIncentivePlanMember_58d19982-2459-4d96-82d4-a9e09184a3b0" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_A2025EquityIncentivePlanMember_50ad146a-a3e0-4d07-9fe0-083bceb822f6" xlink:href="kg-20250930.xsd#kg_A2025EquityIncentivePlanMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PlanNameDomain_ca26f305-c05e-48f1-aea8-c64647f7120d" xlink:to="loc_kg_A2025EquityIncentivePlanMember_50ad146a-a3e0-4d07-9fe0-083bceb822f6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_9c116b77-bb49-4e50-a759-ad45a017192c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable_5208e401-7cc9-4b12-9f44-0a8a4d771ddb" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_9c116b77-bb49-4e50-a759-ad45a017192c" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_9c116b77-bb49-4e50-a759-ad45a017192c_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_9c116b77-bb49-4e50-a759-ad45a017192c" xlink:to="loc_us-gaap_EquityComponentDomain_9c116b77-bb49-4e50-a759-ad45a017192c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_5f0d07ce-5b2c-41cc-83f7-2e346927254e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_9c116b77-bb49-4e50-a759-ad45a017192c" xlink:to="loc_us-gaap_EquityComponentDomain_5f0d07ce-5b2c-41cc-83f7-2e346927254e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_2106d740-5935-4402-9cd8-366b483652d0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_5f0d07ce-5b2c-41cc-83f7-2e346927254e" xlink:to="loc_us-gaap_CommonStockMember_2106d740-5935-4402-9cd8-366b483652d0" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare_494c3821-1266-40f4-8361-d996ddc74f9a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_us-gaap_CommonStockParOrStatedValuePerShare_494c3821-1266-40f4-8361-d996ddc74f9a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationStockConversionRatio_107972f3-0a95-41bd-92e1-a0e12fd481b4" xlink:href="kg-20250930.xsd#kg_BusinessCombinationStockConversionRatio"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_kg_BusinessCombinationStockConversionRatio_107972f3-0a95-41bd-92e1-a0e12fd481b4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_3e366d28-2a92-4c17-a069-645c1cf206cb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_3e366d28-2a92-4c17-a069-645c1cf206cb" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized_ff73e921-fa16-46a6-ac78-80d7a12d687e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_us-gaap_CommonStockSharesAuthorized_ff73e921-fa16-46a6-ac78-80d7a12d687e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockNumberOfVotesPerShare_0f3d6f08-9a87-488a-bdc8-6dfe67988290" xlink:href="kg-20250930.xsd#kg_CommonStockNumberOfVotesPerShare"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_kg_CommonStockNumberOfVotesPerShare_0f3d6f08-9a87-488a-bdc8-6dfe67988290" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ShareCapitalSharesAuthorized_5a67a69b-93e2-4593-9bf9-33d331ec1d14" xlink:href="kg-20250930.xsd#kg_ShareCapitalSharesAuthorized"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_kg_ShareCapitalSharesAuthorized_5a67a69b-93e2-4593-9bf9-33d331ec1d14" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued_6ec8302e-6b2a-4a14-8551-4350b792ca15" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_us-gaap_CommonStockSharesIssued_6ec8302e-6b2a-4a14-8551-4350b792ca15" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding_490e2466-3853-4591-871f-782ebb92d754" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_us-gaap_CommonStockSharesOutstanding_490e2466-3853-4591-871f-782ebb92d754" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares_17329501-6135-45c2-93bc-9f757c8c0d62" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_us-gaap_TreasuryStockCommonShares_17329501-6135-45c2-93bc-9f757c8c0d62" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_00a31e98-9616-4728-bb7d-a2edb1620b15" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_00a31e98-9616-4728-bb7d-a2edb1620b15" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityAwardsExpectedToVestOutstandingNumber_36c529c5-de94-4148-b418-13cef287f9cf" xlink:href="kg-20250930.xsd#kg_EquityAwardsExpectedToVestOutstandingNumber"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_kg_EquityAwardsExpectedToVestOutstandingNumber_36c529c5-de94-4148-b418-13cef287f9cf" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_d0501fa9-f399-4ee0-a34d-5a9b34d4c3ff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ce04b7ab-d8d3-4a57-b1fe-22a35aa1cbf6" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_d0501fa9-f399-4ee0-a34d-5a9b34d4c3ff" xlink:type="arc" order="11"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/ShareholdersEquityScheduleofAccumulatedOtherComprehensiveIncomeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#ShareholdersEquityScheduleofAccumulatedOtherComprehensiveIncomeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/ShareholdersEquityScheduleofAccumulatedOtherComprehensiveIncomeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_e5d9433d-2294-4c1f-8052-9dcbbe141a80" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_d791b7d6-112e-4d56-a925-63bf33c0d076" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_e5d9433d-2294-4c1f-8052-9dcbbe141a80" xlink:to="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_d791b7d6-112e-4d56-a925-63bf33c0d076" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_d758207d-ac6c-491e-9b75-37490d4f2b49" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_d791b7d6-112e-4d56-a925-63bf33c0d076" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_d758207d-ac6c-491e-9b75-37490d4f2b49" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_d758207d-ac6c-491e-9b75-37490d4f2b49_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_d758207d-ac6c-491e-9b75-37490d4f2b49" xlink:to="loc_us-gaap_EquityComponentDomain_d758207d-ac6c-491e-9b75-37490d4f2b49_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_c0ed2532-8958-44da-8741-c5eabbbf9a97" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_d758207d-ac6c-491e-9b75-37490d4f2b49" xlink:to="loc_us-gaap_EquityComponentDomain_c0ed2532-8958-44da-8741-c5eabbbf9a97" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember_eedcbf98-9656-4575-8000-13deb93f1538" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_c0ed2532-8958-44da-8741-c5eabbbf9a97" xlink:to="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember_eedcbf98-9656-4575-8000-13deb93f1538" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_518b45f4-12e4-4e86-8bf1-214e0187e8b5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember_eedcbf98-9656-4575-8000-13deb93f1538" xlink:to="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_518b45f4-12e4-4e86-8bf1-214e0187e8b5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedTranslationAdjustmentMember_8c45fe19-31e9-4c70-8722-0a185bc5f17e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedTranslationAdjustmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember_eedcbf98-9656-4575-8000-13deb93f1538" xlink:to="loc_us-gaap_AccumulatedTranslationAdjustmentMember_8c45fe19-31e9-4c70-8722-0a185bc5f17e" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_41cced26-d1b6-40e6-ba14-81211953aded" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_e5d9433d-2294-4c1f-8052-9dcbbe141a80" xlink:to="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_41cced26-d1b6-40e6-ba14-81211953aded" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_d267a1c0-6d40-4d02-98b8-687650da2f84" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_41cced26-d1b6-40e6-ba14-81211953aded" xlink:to="loc_us-gaap_StockholdersEquity_d267a1c0-6d40-4d02-98b8-687650da2f84" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_a00bbbc1-910e-4226-b29d-d450a3e7f33d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_41cced26-d1b6-40e6-ba14-81211953aded" xlink:to="loc_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_a00bbbc1-910e-4226-b29d-d450a3e7f33d" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_aecf282d-3e15-40a7-8cc0-465742c6c04f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_41cced26-d1b6-40e6-ba14-81211953aded" xlink:to="loc_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_aecf282d-3e15-40a7-8cc0-465742c6c04f" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_ca650fd9-766a-4902-8358-97885486c2c2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_41cced26-d1b6-40e6-ba14-81211953aded" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_ca650fd9-766a-4902-8358-97885486c2c2" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_852c6c55-fe32-4c2c-b844-df09cc1cfa2b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/LongTermDebtNarrativeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#LongTermDebtNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/LongTermDebtNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems_c5b32041-7645-4a93-882a-b6bc25b5adc9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable_40605d39-db7e-457a-a3da-dd665648e1a9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_DebtInstrumentLineItems_c5b32041-7645-4a93-882a-b6bc25b5adc9" xlink:to="loc_us-gaap_DebtInstrumentTable_40605d39-db7e-457a-a3da-dd665648e1a9" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis_75542148-a6f8-414b-9475-ec4fdef55e7c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_40605d39-db7e-457a-a3da-dd665648e1a9" xlink:to="loc_us-gaap_LongtermDebtTypeAxis_75542148-a6f8-414b-9475-ec4fdef55e7c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_75542148-a6f8-414b-9475-ec4fdef55e7c_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_75542148-a6f8-414b-9475-ec4fdef55e7c" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_75542148-a6f8-414b-9475-ec4fdef55e7c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_c043f12d-0cc9-4468-872b-45ceafeb411e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_75542148-a6f8-414b-9475-ec4fdef55e7c" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_c043f12d-0cc9-4468-872b-45ceafeb411e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember_a6ecab75-85c8-4e6a-9c39-3211a0a8ac6f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorNotesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LongtermDebtTypeDomain_c043f12d-0cc9-4468-872b-45ceafeb411e" xlink:to="loc_us-gaap_SeniorNotesMember_a6ecab75-85c8-4e6a-9c39-3211a0a8ac6f" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_1b18e58f-0940-4e4b-b468-299dfb7b087a" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_40605d39-db7e-457a-a3da-dd665648e1a9" xlink:to="loc_srt_RangeAxis_1b18e58f-0940-4e4b-b468-299dfb7b087a" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_1b18e58f-0940-4e4b-b468-299dfb7b087a_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_1b18e58f-0940-4e4b-b468-299dfb7b087a" xlink:to="loc_srt_RangeMember_1b18e58f-0940-4e4b-b468-299dfb7b087a_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_944eb474-3eb4-4cd2-8301-b0b262fe44b9" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_1b18e58f-0940-4e4b-b468-299dfb7b087a" xlink:to="loc_srt_RangeMember_944eb474-3eb4-4cd2-8301-b0b262fe44b9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember_39a980b9-54db-4f1e-ba84-f57b0afd0c7a" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_944eb474-3eb4-4cd2-8301-b0b262fe44b9" xlink:to="loc_srt_MinimumMember_39a980b9-54db-4f1e-ba84-f57b0afd0c7a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_fffbfc16-3dda-44b8-82cc-e99775419e16" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_944eb474-3eb4-4cd2-8301-b0b262fe44b9" xlink:to="loc_srt_MaximumMember_fffbfc16-3dda-44b8-82cc-e99775419e16" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis_2e5ee5cc-6b23-4b30-a5dc-a5a9429e915c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_40605d39-db7e-457a-a3da-dd665648e1a9" xlink:to="loc_us-gaap_DebtInstrumentAxis_2e5ee5cc-6b23-4b30-a5dc-a5a9429e915c" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_2e5ee5cc-6b23-4b30-a5dc-a5a9429e915c_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DebtInstrumentAxis_2e5ee5cc-6b23-4b30-a5dc-a5a9429e915c" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_2e5ee5cc-6b23-4b30-a5dc-a5a9429e915c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_3d86359b-052f-4a70-8d12-910908099ad9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DebtInstrumentAxis_2e5ee5cc-6b23-4b30-a5dc-a5a9429e915c" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_3d86359b-052f-4a70-8d12-910908099ad9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2016Member_3c7de422-cdeb-4a54-aaf4-c6c46b21111a" xlink:href="kg-20250930.xsd#kg_SeniorNotes2016Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_3d86359b-052f-4a70-8d12-910908099ad9" xlink:to="loc_kg_SeniorNotes2016Member_3c7de422-cdeb-4a54-aaf4-c6c46b21111a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2013Member_7450497b-b8e1-48ee-95c3-2d677d3935cb" xlink:href="kg-20250930.xsd#kg_SeniorNotes2013Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_3d86359b-052f-4a70-8d12-910908099ad9" xlink:to="loc_kg_SeniorNotes2013Member_7450497b-b8e1-48ee-95c3-2d677d3935cb" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_d00a239e-9009-45f5-baf9-1553e208a8e3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_c5b32041-7645-4a93-882a-b6bc25b5adc9" xlink:to="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_d00a239e-9009-45f5-baf9-1553e208a8e3" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt_1508acfd-1f19-450d-9eb1-7ccb9e5bfc5f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_c5b32041-7645-4a93-882a-b6bc25b5adc9" xlink:to="loc_us-gaap_InterestExpenseDebt_1508acfd-1f19-450d-9eb1-7ccb9e5bfc5f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrent_237cc31e-0db8-4ac6-b598-2c9b3e9497aa" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPayableCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_c5b32041-7645-4a93-882a-b6bc25b5adc9" xlink:to="loc_us-gaap_InterestPayableCurrent_237cc31e-0db8-4ac6-b598-2c9b3e9497aa" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts_8e31e056-95d4-4db8-847f-cb2b05161ff5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_c5b32041-7645-4a93-882a-b6bc25b5adc9" xlink:to="loc_us-gaap_AmortizationOfFinancingCosts_8e31e056-95d4-4db8-847f-cb2b05161ff5" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPricePercentage_3b77db87-7596-40b6-9041-ce6158bc8014" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPricePercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_c5b32041-7645-4a93-882a-b6bc25b5adc9" xlink:to="loc_us-gaap_DebtInstrumentRedemptionPricePercentage_3b77db87-7596-40b6-9041-ce6158bc8014" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate_139f4bc1-64d5-4bcf-a8d8-6ffbc3fe0dae" xlink:href="kg-20250930.xsd#kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_c5b32041-7645-4a93-882a-b6bc25b5adc9" xlink:to="loc_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate_139f4bc1-64d5-4bcf-a8d8-6ffbc3fe0dae" xlink:type="arc" order="5"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/LongTermDebtScheduleofIssuancesofSeniorNotesOutstandingDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#LongTermDebtScheduleofIssuancesofSeniorNotesOutstandingDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/LongTermDebtScheduleofIssuancesofSeniorNotesOutstandingDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems_bed8c346-fe28-455d-86e0-6ec8b2ce31c1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable_a578f5d5-3f75-4fca-987a-a42c477e05e3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_DebtInstrumentLineItems_bed8c346-fe28-455d-86e0-6ec8b2ce31c1" xlink:to="loc_us-gaap_DebtInstrumentTable_a578f5d5-3f75-4fca-987a-a42c477e05e3" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis_26918dce-37e2-49d6-a8d4-3e05c80d9a67" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_a578f5d5-3f75-4fca-987a-a42c477e05e3" xlink:to="loc_us-gaap_LongtermDebtTypeAxis_26918dce-37e2-49d6-a8d4-3e05c80d9a67" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_26918dce-37e2-49d6-a8d4-3e05c80d9a67_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_26918dce-37e2-49d6-a8d4-3e05c80d9a67" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_26918dce-37e2-49d6-a8d4-3e05c80d9a67_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_a0ebfc3b-a565-44f1-a671-3788b323ef0c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_26918dce-37e2-49d6-a8d4-3e05c80d9a67" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_a0ebfc3b-a565-44f1-a671-3788b323ef0c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember_90b60026-916b-4c0c-b583-3fdedb45b87c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorNotesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LongtermDebtTypeDomain_a0ebfc3b-a565-44f1-a671-3788b323ef0c" xlink:to="loc_us-gaap_SeniorNotesMember_90b60026-916b-4c0c-b583-3fdedb45b87c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis_1d46b496-1085-4875-86be-ce9cdd55cbcf" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_a578f5d5-3f75-4fca-987a-a42c477e05e3" xlink:to="loc_us-gaap_DebtInstrumentAxis_1d46b496-1085-4875-86be-ce9cdd55cbcf" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_1d46b496-1085-4875-86be-ce9cdd55cbcf_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DebtInstrumentAxis_1d46b496-1085-4875-86be-ce9cdd55cbcf" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_1d46b496-1085-4875-86be-ce9cdd55cbcf_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_6120aff4-5110-49b3-915c-e239c1893684" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DebtInstrumentAxis_1d46b496-1085-4875-86be-ce9cdd55cbcf" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_6120aff4-5110-49b3-915c-e239c1893684" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2016Member_3f7aca13-3b86-45ee-a71e-671282606ba4" xlink:href="kg-20250930.xsd#kg_SeniorNotes2016Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_6120aff4-5110-49b3-915c-e239c1893684" xlink:to="loc_kg_SeniorNotes2016Member_3f7aca13-3b86-45ee-a71e-671282606ba4" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2013Member_c0ecc408-09da-4a03-b110-79708e84abb4" xlink:href="kg-20250930.xsd#kg_SeniorNotes2013Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_6120aff4-5110-49b3-915c-e239c1893684" xlink:to="loc_kg_SeniorNotes2013Member_c0ecc408-09da-4a03-b110-79708e84abb4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount_0c88f544-d832-44e3-b26e-1aa506b99b4a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_bed8c346-fe28-455d-86e0-6ec8b2ce31c1" xlink:to="loc_us-gaap_DebtInstrumentCarryingAmount_0c88f544-d832-44e3-b26e-1aa506b99b4a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet_25aa9fdc-da7c-49b7-aa19-69b022b52450" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_bed8c346-fe28-455d-86e0-6ec8b2ce31c1" xlink:to="loc_us-gaap_DeferredFinanceCostsNet_25aa9fdc-da7c-49b7-aa19-69b022b52450" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt_977faee8-10fc-44c8-af6f-5a6374b61ac7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_bed8c346-fe28-455d-86e0-6ec8b2ce31c1" xlink:to="loc_us-gaap_LongTermDebt_977faee8-10fc-44c8-af6f-5a6374b61ac7" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsGross_2fab981e-16d2-4bc6-9bbb-cbe67c582617" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsGross"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_bed8c346-fe28-455d-86e0-6ec8b2ce31c1" xlink:to="loc_us-gaap_DeferredFinanceCostsGross_2fab981e-16d2-4bc6-9bbb-cbe67c582617" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_87dd1017-7950-4597-a207-de381e4d8eb1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_bed8c346-fe28-455d-86e0-6ec8b2ce31c1" xlink:to="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_87dd1017-7950-4597-a207-de381e4d8eb1" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage_ff106ef7-f8bf-44d8-b318-b0568ddf5a53" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_bed8c346-fe28-455d-86e0-6ec8b2ce31c1" xlink:to="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage_ff106ef7-f8bf-44d8-b318-b0568ddf5a53" xlink:type="arc" order="5"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/ReinsuranceNarrativeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#ReinsuranceNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/ReinsuranceNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRetentionPolicyLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionPolicyTable_2c30634c-315e-4e11-bf71-69beef08b3fe" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRetentionPolicyTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_us-gaap_ReinsuranceRetentionPolicyTable_2c30634c-315e-4e11-bf71-69beef08b3fe" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_85ecf5bb-314d-4852-969d-afc4ca856b4e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyTable_2c30634c-315e-4e11-bf71-69beef08b3fe" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_85ecf5bb-314d-4852-969d-afc4ca856b4e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_85ecf5bb-314d-4852-969d-afc4ca856b4e_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_85ecf5bb-314d-4852-969d-afc4ca856b4e" xlink:to="loc_us-gaap_SegmentDomain_85ecf5bb-314d-4852-969d-afc4ca856b4e_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_302b29a3-d67b-46d2-ba0d-7cbf09ea5fcf" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_85ecf5bb-314d-4852-969d-afc4ca856b4e" xlink:to="loc_us-gaap_SegmentDomain_302b29a3-d67b-46d2-ba0d-7cbf09ea5fcf" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DiversifiedReinsuranceSegmentMember_bdced6f1-53c7-4de3-b1a1-797b95b3b868" xlink:href="kg-20250930.xsd#kg_DiversifiedReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_302b29a3-d67b-46d2-ba0d-7cbf09ea5fcf" xlink:to="loc_kg_DiversifiedReinsuranceSegmentMember_bdced6f1-53c7-4de3-b1a1-797b95b3b868" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustReinsuranceSegmentMember_011bcee6-1da5-4744-a5f2-45ff5b18babb" xlink:href="kg-20250930.xsd#kg_AmTrustReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_302b29a3-d67b-46d2-ba0d-7cbf09ea5fcf" xlink:to="loc_kg_AmTrustReinsuranceSegmentMember_011bcee6-1da5-4744-a5f2-45ff5b18babb" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_8297c229-b64a-4d13-9d59-0515cb4434ac" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyTable_2c30634c-315e-4e11-bf71-69beef08b3fe" xlink:to="loc_srt_RangeAxis_8297c229-b64a-4d13-9d59-0515cb4434ac" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_8297c229-b64a-4d13-9d59-0515cb4434ac_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_8297c229-b64a-4d13-9d59-0515cb4434ac" xlink:to="loc_srt_RangeMember_8297c229-b64a-4d13-9d59-0515cb4434ac_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_079e00bc-003b-4a7a-9f76-b1a9d2cfe52f" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_8297c229-b64a-4d13-9d59-0515cb4434ac" xlink:to="loc_srt_RangeMember_079e00bc-003b-4a7a-9f76-b1a9d2cfe52f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_94a6545c-a2a6-48d9-88a3-8656daae9269" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_079e00bc-003b-4a7a-9f76-b1a9d2cfe52f" xlink:to="loc_srt_MaximumMember_94a6545c-a2a6-48d9-88a3-8656daae9269" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskAxis_7ab8404c-46b3-43f0-8086-9791c17ddade" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyTable_2c30634c-315e-4e11-bf71-69beef08b3fe" xlink:to="loc_us-gaap_CededCreditRiskAxis_7ab8404c-46b3-43f0-8086-9791c17ddade" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain_7ab8404c-46b3-43f0-8086-9791c17ddade_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_CededCreditRiskAxis_7ab8404c-46b3-43f0-8086-9791c17ddade" xlink:to="loc_us-gaap_CededCreditRiskReinsurerDomain_7ab8404c-46b3-43f0-8086-9791c17ddade_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain_f690f6d1-8273-4a39-b129-06530ddab34b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_CededCreditRiskAxis_7ab8404c-46b3-43f0-8086-9791c17ddade" xlink:to="loc_us-gaap_CededCreditRiskReinsurerDomain_f690f6d1-8273-4a39-b129-06530ddab34b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CavelloMember_7fdb304d-1e8f-4066-b7c7-ff3a40132b7c" xlink:href="kg-20250930.xsd#kg_CavelloMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain_f690f6d1-8273-4a39-b129-06530ddab34b" xlink:to="loc_kg_CavelloMember_7fdb304d-1e8f-4066-b7c7-ff3a40132b7c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_68de32e9-ddaf-4002-ba98-06f4033235c6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_68de32e9-ddaf-4002-ba98-06f4033235c6" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesAllowance_bb276c3a-15c8-41bd-97a8-027e23b51419" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesAllowance"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_us-gaap_ReinsuranceRecoverablesAllowance_bb276c3a-15c8-41bd-97a8-027e23b51419" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage_ff7c60a4-8798-446d-a1db-d79729b30528" xlink:href="kg-20250930.xsd#kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage_ff7c60a4-8798-446d-a1db-d79729b30528" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy_fc1855c9-ec84-476c-a4de-f83a1725456a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy_fc1855c9-ec84-476c-a4de-f83a1725456a" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy_01685e9c-00be-47d9-8882-021d0be2a4fd" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy_01685e9c-00be-47d9-8882-021d0be2a4fd" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover_25ecb83f-904a-41df-af73-fceb42b4460e" xlink:href="kg-20250930.xsd#kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover_25ecb83f-904a-41df-af73-fceb42b4460e" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross_5c66d6c6-9917-4ac3-b4c2-f6f2a6c2f148" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross_5c66d6c6-9917-4ac3-b4c2-f6f2a6c2f148" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceCollateralByThirdParty_7506cca6-4f80-423a-80b3-a8925fc24f5d" xlink:href="kg-20250930.xsd#kg_ReinsuranceCollateralByThirdParty"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_kg_ReinsuranceCollateralByThirdParty_7506cca6-4f80-423a-80b3-a8925fc24f5d" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross_f69dedbb-3ef2-4ef3-bde0-73dd08e18e8c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesOnPaidLossesGross"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross_f69dedbb-3ef2-4ef3-bde0-73dd08e18e8c" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims_798d1643-2177-4c5b-95bf-133596e4df51" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems_2d3db2f3-42cd-44a4-a19e-288185b5eed8" xlink:to="loc_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims_798d1643-2177-4c5b-95bf-133596e4df51" xlink:type="arc" order="9"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/ReserveforLossandLossAdjustmentExpensesScheduleofDevelopmentExperiencedDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#ReserveforLossandLossAdjustmentExpensesScheduleofDevelopmentExperiencedDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/ReserveforLossandLossAdjustmentExpensesScheduleofDevelopmentExperiencedDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems_2abd261d-0f51-440e-bc10-a59d992e00db" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_b9e3897a-1969-4f20-9fe5-b63592dd72a0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_2abd261d-0f51-440e-bc10-a59d992e00db" xlink:to="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_b9e3897a-1969-4f20-9fe5-b63592dd72a0" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_921a06a6-329f-4a07-83fa-e5b0d47dbe88" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_b9e3897a-1969-4f20-9fe5-b63592dd72a0" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_921a06a6-329f-4a07-83fa-e5b0d47dbe88" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_921a06a6-329f-4a07-83fa-e5b0d47dbe88_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_921a06a6-329f-4a07-83fa-e5b0d47dbe88" xlink:to="loc_us-gaap_SegmentDomain_921a06a6-329f-4a07-83fa-e5b0d47dbe88_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_1bc49db1-62df-4fb7-a345-258902332ed0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_921a06a6-329f-4a07-83fa-e5b0d47dbe88" xlink:to="loc_us-gaap_SegmentDomain_1bc49db1-62df-4fb7-a345-258902332ed0" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DiversifiedReinsuranceSegmentMember_c7ca2c91-7506-475f-b838-c3b2526f65c2" xlink:href="kg-20250930.xsd#kg_DiversifiedReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_1bc49db1-62df-4fb7-a345-258902332ed0" xlink:to="loc_kg_DiversifiedReinsuranceSegmentMember_c7ca2c91-7506-475f-b838-c3b2526f65c2" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustReinsuranceSegmentMember_bb3ab1c5-e3c2-4f0d-9ed8-afc91e20f353" xlink:href="kg-20250930.xsd#kg_AmTrustReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_1bc49db1-62df-4fb7-a345-258902332ed0" xlink:to="loc_kg_AmTrustReinsuranceSegmentMember_bb3ab1c5-e3c2-4f0d-9ed8-afc91e20f353" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_feda2351-b688-47ea-a59f-05a343a6b5f3" xlink:href="kg-20250930.xsd#kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_2abd261d-0f51-440e-bc10-a59d992e00db" xlink:to="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_feda2351-b688-47ea-a59f-05a343a6b5f3" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/ReserveforLossandLossAdjustmentExpensesNarrativeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#ReserveforLossandLossAdjustmentExpensesNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/ReserveforLossandLossAdjustmentExpensesNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems_a74df38c-7dc1-4473-a8f9-2ba31897dfde" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_a1290fc3-55f2-4c9e-82e4-c4eafc3e79a9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_a74df38c-7dc1-4473-a8f9-2ba31897dfde" xlink:to="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_a1290fc3-55f2-4c9e-82e4-c4eafc3e79a9" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_2d21943e-dcae-4c04-bea1-35e29e14ce08" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_a1290fc3-55f2-4c9e-82e4-c4eafc3e79a9" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_2d21943e-dcae-4c04-bea1-35e29e14ce08" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_2d21943e-dcae-4c04-bea1-35e29e14ce08_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_2d21943e-dcae-4c04-bea1-35e29e14ce08" xlink:to="loc_us-gaap_SegmentDomain_2d21943e-dcae-4c04-bea1-35e29e14ce08_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_54cead9c-bc17-41eb-b0a9-7cc078978f93" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_2d21943e-dcae-4c04-bea1-35e29e14ce08" xlink:to="loc_us-gaap_SegmentDomain_54cead9c-bc17-41eb-b0a9-7cc078978f93" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DiversifiedReinsuranceSegmentMember_2594e0ea-9271-40d7-8429-6c3bcbfcd131" xlink:href="kg-20250930.xsd#kg_DiversifiedReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_54cead9c-bc17-41eb-b0a9-7cc078978f93" xlink:to="loc_kg_DiversifiedReinsuranceSegmentMember_2594e0ea-9271-40d7-8429-6c3bcbfcd131" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_7ed2d3d9-3e31-4315-9c5a-7cd0d6fbdb53" xlink:href="kg-20250930.xsd#kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_a74df38c-7dc1-4473-a8f9-2ba31897dfde" xlink:to="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_7ed2d3d9-3e31-4315-9c5a-7cd0d6fbdb53" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/ReserveforLossandLossAdjustmentExpensesScheduleofPriorYearLossDevelopmentfortheAmTrustReinsuranceSegmentDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#ReserveforLossandLossAdjustmentExpensesScheduleofPriorYearLossDevelopmentfortheAmTrustReinsuranceSegmentDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/ReserveforLossandLossAdjustmentExpensesScheduleofPriorYearLossDevelopmentfortheAmTrustReinsuranceSegmentDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems_dc97f8a8-0036-49d8-884f-aaf737f5bf38" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_b566c222-0f58-4d84-bab9-a39f6f6c90ec" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_dc97f8a8-0036-49d8-884f-aaf737f5bf38" xlink:to="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_b566c222-0f58-4d84-bab9-a39f6f6c90ec" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_e138414a-644b-4eed-9a9d-4addb90a265a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_b566c222-0f58-4d84-bab9-a39f6f6c90ec" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_e138414a-644b-4eed-9a9d-4addb90a265a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_e138414a-644b-4eed-9a9d-4addb90a265a_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_e138414a-644b-4eed-9a9d-4addb90a265a" xlink:to="loc_us-gaap_SegmentDomain_e138414a-644b-4eed-9a9d-4addb90a265a_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_4f7784df-881e-47b7-ae50-394fe462fa18" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_e138414a-644b-4eed-9a9d-4addb90a265a" xlink:to="loc_us-gaap_SegmentDomain_4f7784df-881e-47b7-ae50-394fe462fa18" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustReinsuranceSegmentMember_da6d60b2-1b44-48d3-bb82-8d313957d012" xlink:href="kg-20250930.xsd#kg_AmTrustReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_4f7784df-881e-47b7-ae50-394fe462fa18" xlink:to="loc_kg_AmTrustReinsuranceSegmentMember_da6d60b2-1b44-48d3-bb82-8d313957d012" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis_5d96c49f-e867-4700-8c34-930f10691782" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductOrServiceAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_b566c222-0f58-4d84-bab9-a39f6f6c90ec" xlink:to="loc_srt_ProductOrServiceAxis_5d96c49f-e867-4700-8c34-930f10691782" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain_5d96c49f-e867-4700-8c34-930f10691782_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ProductOrServiceAxis_5d96c49f-e867-4700-8c34-930f10691782" xlink:to="loc_srt_ProductsAndServicesDomain_5d96c49f-e867-4700-8c34-930f10691782_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain_17b675fe-5322-4a81-b24d-ee244f3a8a45" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ProductOrServiceAxis_5d96c49f-e867-4700-8c34-930f10691782" xlink:to="loc_srt_ProductsAndServicesDomain_17b675fe-5322-4a81-b24d-ee244f3a8a45" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustQuotaShareMember_d529fdfc-0eb2-4479-97ff-7a92f830c0bb" xlink:href="kg-20250930.xsd#kg_AmTrustQuotaShareMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_17b675fe-5322-4a81-b24d-ee244f3a8a45" xlink:to="loc_kg_AmTrustQuotaShareMember_d529fdfc-0eb2-4479-97ff-7a92f830c0bb" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LPTADCAgreementMember_7af3782e-9a3e-4d4d-beaf-7bdf04b94535" xlink:href="kg-20250930.xsd#kg_LPTADCAgreementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_17b675fe-5322-4a81-b24d-ee244f3a8a45" xlink:to="loc_kg_LPTADCAgreementMember_7af3782e-9a3e-4d4d-beaf-7bdf04b94535" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_a5432643-9bba-4cf8-876d-c90e0613169f" xlink:href="kg-20250930.xsd#kg_EuropeanHospitalLiabilityQuotaShareAgreementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_17b675fe-5322-4a81-b24d-ee244f3a8a45" xlink:to="loc_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_a5432643-9bba-4cf8-876d-c90e0613169f" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_474a586f-4032-471f-b959-f59ee23670a0" xlink:href="kg-20250930.xsd#kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_dc97f8a8-0036-49d8-884f-aaf737f5bf38" xlink:to="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_474a586f-4032-471f-b959-f59ee23670a0" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/RelatedPartyTransactionsNarrativeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#RelatedPartyTransactionsNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/RelatedPartyTransactionsNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_b4827423-b4e4-43c1-9d49-cdf0b370342d" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_b4827423-b4e4-43c1-9d49-cdf0b370342d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_b4827423-b4e4-43c1-9d49-cdf0b370342d_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_b4827423-b4e4-43c1-9d49-cdf0b370342d" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_b4827423-b4e4-43c1-9d49-cdf0b370342d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_6950f723-db20-4a42-b707-1f857f52e97b" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_b4827423-b4e4-43c1-9d49-cdf0b370342d" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_6950f723-db20-4a42-b707-1f857f52e97b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_d5cf9019-8cec-4fb3-954b-a728f443d6df" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_6950f723-db20-4a42-b707-1f857f52e97b" xlink:to="loc_kg_KestrelGroupLtd.Member_d5cf9019-8cec-4fb3-954b-a728f443d6df" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BarryZyskindMember_43dc2834-9ddf-423b-be70-81c0e5518abc" xlink:href="kg-20250930.xsd#kg_BarryZyskindMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_6950f723-db20-4a42-b707-1f857f52e97b" xlink:to="loc_kg_BarryZyskindMember_43dc2834-9ddf-423b-be70-81c0e5518abc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GeorgeKarfunkelMember_177f8190-e00f-4649-b982-03fac7781c92" xlink:href="kg-20250930.xsd#kg_GeorgeKarfunkelMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_6950f723-db20-4a42-b707-1f857f52e97b" xlink:to="loc_kg_GeorgeKarfunkelMember_177f8190-e00f-4649-b982-03fac7781c92" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LeahKarfunkelMember_3e7dde64-d6ae-4e29-86dc-bdee254fa616" xlink:href="kg-20250930.xsd#kg_LeahKarfunkelMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_6950f723-db20-4a42-b707-1f857f52e97b" xlink:to="loc_kg_LeahKarfunkelMember_3e7dde64-d6ae-4e29-86dc-bdee254fa616" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember_5bd2cb15-dd8d-4836-90f8-f452fe29bc87" xlink:href="kg-20250930.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_6950f723-db20-4a42-b707-1f857f52e97b" xlink:to="loc_kg_AmtrustFinancialServicesIncMember_5bd2cb15-dd8d-4836-90f8-f452fe29bc87" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis_273604a2-3ff4-4672-8615-a68f0aed56b7" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_dei_LegalEntityAxis_273604a2-3ff4-4672-8615-a68f0aed56b7" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_273604a2-3ff4-4672-8615-a68f0aed56b7_default" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_dei_LegalEntityAxis_273604a2-3ff4-4672-8615-a68f0aed56b7" xlink:to="loc_dei_EntityDomain_273604a2-3ff4-4672-8615-a68f0aed56b7_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_53cb45f5-eec8-4d08-be76-498f4a180688" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_dei_LegalEntityAxis_273604a2-3ff4-4672-8615-a68f0aed56b7" xlink:to="loc_dei_EntityDomain_53cb45f5-eec8-4d08-be76-498f4a180688" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember_2c04182f-9b9b-4a18-81e1-600fe4500d9b" xlink:href="kg-20250930.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_53cb45f5-eec8-4d08-be76-498f4a180688" xlink:to="loc_kg_AmtrustFinancialServicesIncMember_2c04182f-9b9b-4a18-81e1-600fe4500d9b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KILHMember_43995399-4d2b-4e0a-9857-cb812799e199" xlink:href="kg-20250930.xsd#kg_KILHMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_53cb45f5-eec8-4d08-be76-498f4a180688" xlink:to="loc_kg_KILHMember_43995399-4d2b-4e0a-9857-cb812799e199" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustNorthAmericaIncMember_cfbd1654-a17b-4836-a2e1-ad2435909fc4" xlink:href="kg-20250930.xsd#kg_AmTrustNorthAmericaIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_53cb45f5-eec8-4d08-be76-498f4a180688" xlink:to="loc_kg_AmTrustNorthAmericaIncMember_cfbd1654-a17b-4836-a2e1-ad2435909fc4" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupMember_04ea9394-e0ed-446b-aa4b-bcccb4c692b4" xlink:href="kg-20250930.xsd#kg_KestrelGroupMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_53cb45f5-eec8-4d08-be76-498f4a180688" xlink:to="loc_kg_KestrelGroupMember_04ea9394-e0ed-446b-aa4b-bcccb4c692b4" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MaidenReinsuranceMember_9db618ca-c013-4466-9c24-b9321bc84b54" xlink:href="kg-20250930.xsd#kg_MaidenReinsuranceMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_53cb45f5-eec8-4d08-be76-498f4a180688" xlink:to="loc_kg_MaidenReinsuranceMember_9db618ca-c013-4466-9c24-b9321bc84b54" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis_78eceb5c-8169-4b8e-8f28-42bee58046d2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_us-gaap_BusinessAcquisitionAxis_78eceb5c-8169-4b8e-8f28-42bee58046d2" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_78eceb5c-8169-4b8e-8f28-42bee58046d2_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_78eceb5c-8169-4b8e-8f28-42bee58046d2" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_78eceb5c-8169-4b8e-8f28-42bee58046d2_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_06d30d6b-da6f-4a56-9a81-302cef1fd7bc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_78eceb5c-8169-4b8e-8f28-42bee58046d2" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_06d30d6b-da6f-4a56-9a81-302cef1fd7bc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_def8301c-ce7a-4d18-8d52-890e41a18e0c" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain_06d30d6b-da6f-4a56-9a81-302cef1fd7bc" xlink:to="loc_kg_KestrelGroupLtd.Member_def8301c-ce7a-4d18-8d52-890e41a18e0c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_afe54c38-38a0-4362-9499-941bf705560a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_afe54c38-38a0-4362-9499-941bf705560a" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_afe54c38-38a0-4362-9499-941bf705560a_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_afe54c38-38a0-4362-9499-941bf705560a" xlink:to="loc_us-gaap_EquityComponentDomain_afe54c38-38a0-4362-9499-941bf705560a_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_a0839336-1670-48c6-b597-6f6e8c34eb3c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_afe54c38-38a0-4362-9499-941bf705560a" xlink:to="loc_us-gaap_EquityComponentDomain_a0839336-1670-48c6-b597-6f6e8c34eb3c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_c59ef3cb-e138-46ed-aa04-ca474b03c7d7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_a0839336-1670-48c6-b597-6f6e8c34eb3c" xlink:to="loc_us-gaap_CommonStockMember_c59ef3cb-e138-46ed-aa04-ca474b03c7d7" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis_a75e2e70-c27d-4d85-8e19-a003bdb5e36d" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_srt_OwnershipAxis_a75e2e70-c27d-4d85-8e19-a003bdb5e36d" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain_a75e2e70-c27d-4d85-8e19-a003bdb5e36d_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_OwnershipAxis_a75e2e70-c27d-4d85-8e19-a003bdb5e36d" xlink:to="loc_srt_OwnershipDomain_a75e2e70-c27d-4d85-8e19-a003bdb5e36d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain_d44dba8a-61f1-47ed-bfda-3cec3a41410b" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_OwnershipAxis_a75e2e70-c27d-4d85-8e19-a003bdb5e36d" xlink:to="loc_srt_OwnershipDomain_d44dba8a-61f1-47ed-bfda-3cec3a41410b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_e8544109-ec36-4d95-95cd-07dac9386e39" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_OwnershipDomain_d44dba8a-61f1-47ed-bfda-3cec3a41410b" xlink:to="loc_kg_KestrelGroupLtd.Member_e8544109-ec36-4d95-95cd-07dac9386e39" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember_2f2ea82d-4172-410e-93a1-10a65b158e54" xlink:href="kg-20250930.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_OwnershipDomain_d44dba8a-61f1-47ed-bfda-3cec3a41410b" xlink:to="loc_kg_AmtrustFinancialServicesIncMember_2f2ea82d-4172-410e-93a1-10a65b158e54" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustNorthAmericaIncMember_6d3aea87-f663-4174-87b3-6cf30fec6a92" xlink:href="kg-20250930.xsd#kg_AmTrustNorthAmericaIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_OwnershipDomain_d44dba8a-61f1-47ed-bfda-3cec3a41410b" xlink:to="loc_kg_AmTrustNorthAmericaIncMember_6d3aea87-f663-4174-87b3-6cf30fec6a92" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis_e8624874-4810-43d5-8a38-0399af3d5026" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_us-gaap_RelatedPartyTransactionAxis_e8624874-4810-43d5-8a38-0399af3d5026" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain_e8624874-4810-43d5-8a38-0399af3d5026_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis_e8624874-4810-43d5-8a38-0399af3d5026" xlink:to="loc_us-gaap_RelatedPartyTransactionDomain_e8624874-4810-43d5-8a38-0399af3d5026_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis_e8624874-4810-43d5-8a38-0399af3d5026" xlink:to="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementMaximumLossCorridorMember_d7ad950a-34e8-49f6-b6aa-38390fd02b19" xlink:href="kg-20250930.xsd#kg_PostTerminationEndorsementMaximumLossCorridorMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:to="loc_kg_PostTerminationEndorsementMaximumLossCorridorMember_d7ad950a-34e8-49f6-b6aa-38390fd02b19" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember_9abb29e4-0b37-4ca0-a03a-768ac2791d51" xlink:href="kg-20250930.xsd#kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:to="loc_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember_9abb29e4-0b37-4ca0-a03a-768ac2791d51" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementMember_274b5595-4219-4dac-9b7f-9635b981fff6" xlink:href="kg-20250930.xsd#kg_PostTerminationEndorsementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:to="loc_kg_PostTerminationEndorsementMember_274b5595-4219-4dac-9b7f-9635b981fff6" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember_13154afb-0a43-465a-a351-73874761d4c1" xlink:href="kg-20250930.xsd#kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:to="loc_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember_13154afb-0a43-465a-a351-73874761d4c1" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementNo.2Member_88938ada-41e2-4927-aea6-738b5fb8aa17" xlink:href="kg-20250930.xsd#kg_PostTerminationEndorsementNo.2Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:to="loc_kg_PostTerminationEndorsementNo.2Member_88938ada-41e2-4927-aea6-738b5fb8aa17" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementNo.1Member_c3f7600d-489d-4ce5-b29f-75363204f98a" xlink:href="kg-20250930.xsd#kg_PostTerminationEndorsementNo.1Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:to="loc_kg_PostTerminationEndorsementNo.1Member_c3f7600d-489d-4ce5-b29f-75363204f98a" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PremiumRepaymentLoanAgreementMember_cd5ba382-c5f1-43cd-adbb-797024fd030d" xlink:href="kg-20250930.xsd#kg_PremiumRepaymentLoanAgreementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:to="loc_kg_PremiumRepaymentLoanAgreementMember_cd5ba382-c5f1-43cd-adbb-797024fd030d" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember_9a0419ac-28aa-4b8e-9b22-2816a9f6e289" xlink:href="kg-20250930.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_323bae8b-5910-45ac-b7b4-6282595fa28b" xlink:to="loc_kg_AmtrustFinancialServicesIncMember_9a0419ac-28aa-4b8e-9b22-2816a9f6e289" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_c651a564-808b-4014-8000-a6f00c34123b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_c651a564-808b-4014-8000-a6f00c34123b" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_c651a564-808b-4014-8000-a6f00c34123b_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_c651a564-808b-4014-8000-a6f00c34123b" xlink:to="loc_us-gaap_RelatedPartyDomain_c651a564-808b-4014-8000-a6f00c34123b_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_1bfd4c72-16b2-4ac4-a3bb-c0855fb00af6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_c651a564-808b-4014-8000-a6f00c34123b" xlink:to="loc_us-gaap_RelatedPartyDomain_1bfd4c72-16b2-4ac4-a3bb-c0855fb00af6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FoundingShareholdersMember_95e27758-aee1-4ec2-bd73-fd28c54c73a5" xlink:href="kg-20250930.xsd#kg_FoundingShareholdersMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyDomain_1bfd4c72-16b2-4ac4-a3bb-c0855fb00af6" xlink:to="loc_kg_FoundingShareholdersMember_95e27758-aee1-4ec2-bd73-fd28c54c73a5" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember_1852b11d-0322-49d8-a46f-bfe3fc5689ed" xlink:href="kg-20250930.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyDomain_1bfd4c72-16b2-4ac4-a3bb-c0855fb00af6" xlink:to="loc_kg_AmtrustFinancialServicesIncMember_1852b11d-0322-49d8-a46f-bfe3fc5689ed" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustNorthAmericaIncMember_54788dc6-66ec-4ae1-bceb-87b57fd76aaa" xlink:href="kg-20250930.xsd#kg_AmTrustNorthAmericaIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyDomain_1bfd4c72-16b2-4ac4-a3bb-c0855fb00af6" xlink:to="loc_kg_AmTrustNorthAmericaIncMember_54788dc6-66ec-4ae1-bceb-87b57fd76aaa" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelIntermediateLedbetterHoldingsMember_86f38bf8-d060-4125-a884-8759799407e2" xlink:href="kg-20250930.xsd#kg_KestrelIntermediateLedbetterHoldingsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyDomain_1bfd4c72-16b2-4ac4-a3bb-c0855fb00af6" xlink:to="loc_kg_KestrelIntermediateLedbetterHoldingsMember_86f38bf8-d060-4125-a884-8759799407e2" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AELMember_3643d865-ff74-4933-a5b8-cce80adecf6c" xlink:href="kg-20250930.xsd#kg_AELMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyDomain_1bfd4c72-16b2-4ac4-a3bb-c0855fb00af6" xlink:to="loc_kg_AELMember_3643d865-ff74-4933-a5b8-cce80adecf6c" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TypeOfArrangementAxis_3801b1aa-69c5-4835-82e8-b71363d9bcf0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfArrangementAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_us-gaap_TypeOfArrangementAxis_3801b1aa-69c5-4835-82e8-b71363d9bcf0" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_3801b1aa-69c5-4835-82e8-b71363d9bcf0_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_TypeOfArrangementAxis_3801b1aa-69c5-4835-82e8-b71363d9bcf0" xlink:to="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_3801b1aa-69c5-4835-82e8-b71363d9bcf0_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_2ce35e1f-5f9a-4a5d-a88a-80289064f6f4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_TypeOfArrangementAxis_3801b1aa-69c5-4835-82e8-b71363d9bcf0" xlink:to="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_2ce35e1f-5f9a-4a5d-a88a-80289064f6f4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustQuotaShareReinsuranceSegmentMember_609d8cfa-d871-4736-bab2-3bd730d28b80" xlink:href="kg-20250930.xsd#kg_AmtrustQuotaShareReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_2ce35e1f-5f9a-4a5d-a88a-80289064f6f4" xlink:to="loc_kg_AmtrustQuotaShareReinsuranceSegmentMember_609d8cfa-d871-4736-bab2-3bd730d28b80" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_c2395c65-1a58-45b5-ae1e-f6fb8393be52" xlink:href="kg-20250930.xsd#kg_EuropeanHospitalLiabilityQuotaShareAgreementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_2ce35e1f-5f9a-4a5d-a88a-80289064f6f4" xlink:to="loc_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_c2395c65-1a58-45b5-ae1e-f6fb8393be52" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember_0cfcc0af-6a6d-48f4-8f34-782326196e01" xlink:href="kg-20250930.xsd#kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_2ce35e1f-5f9a-4a5d-a88a-80289064f6f4" xlink:to="loc_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember_0cfcc0af-6a6d-48f4-8f34-782326196e01" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetManagementAgreementMember_4e4f1772-33ae-49a8-9592-657575e962cb" xlink:href="kg-20250930.xsd#kg_AssetManagementAgreementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_2ce35e1f-5f9a-4a5d-a88a-80289064f6f4" xlink:to="loc_kg_AssetManagementAgreementMember_4e4f1772-33ae-49a8-9592-657575e962cb" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_bb0c67d7-20da-456f-90c0-924d6763b9fa" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_srt_RangeAxis_bb0c67d7-20da-456f-90c0-924d6763b9fa" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_bb0c67d7-20da-456f-90c0-924d6763b9fa_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_bb0c67d7-20da-456f-90c0-924d6763b9fa" xlink:to="loc_srt_RangeMember_bb0c67d7-20da-456f-90c0-924d6763b9fa_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_e69fd966-4133-46c6-9fb4-42dc28d71081" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_bb0c67d7-20da-456f-90c0-924d6763b9fa" xlink:to="loc_srt_RangeMember_e69fd966-4133-46c6-9fb4-42dc28d71081" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember_86aabb30-f7e4-4fdd-b2e1-2aabebb150fc" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_e69fd966-4133-46c6-9fb4-42dc28d71081" xlink:to="loc_srt_MinimumMember_86aabb30-f7e4-4fdd-b2e1-2aabebb150fc" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_f2294a84-9123-45ac-b545-32f5a658f27e" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_e69fd966-4133-46c6-9fb4-42dc28d71081" xlink:to="loc_srt_MaximumMember_f2294a84-9123-45ac-b545-32f5a658f27e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_95eaaad2-106d-4dea-bfa4-306763598fe0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_95eaaad2-106d-4dea-bfa4-306763598fe0" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_95eaaad2-106d-4dea-bfa4-306763598fe0_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_95eaaad2-106d-4dea-bfa4-306763598fe0" xlink:to="loc_us-gaap_SegmentDomain_95eaaad2-106d-4dea-bfa4-306763598fe0_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_cbff5b86-fbfa-48cd-99c6-2e34652799f9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_95eaaad2-106d-4dea-bfa4-306763598fe0" xlink:to="loc_us-gaap_SegmentDomain_cbff5b86-fbfa-48cd-99c6-2e34652799f9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustReinsuranceSegmentMember_1af6240f-2886-48af-9eef-61b24e61a416" xlink:href="kg-20250930.xsd#kg_AmTrustReinsuranceSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_cbff5b86-fbfa-48cd-99c6-2e34652799f9" xlink:to="loc_kg_AmTrustReinsuranceSegmentMember_1af6240f-2886-48af-9eef-61b24e61a416" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionByTypeAxis_5605d569-5c3c-4da2-81f4-d42f7a53d591" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionByTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_kg_RelatedPartyTransactionByTypeAxis_5605d569-5c3c-4da2-81f4-d42f7a53d591" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionByTypeDomain_5605d569-5c3c-4da2-81f4-d42f7a53d591_default" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionByTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_kg_RelatedPartyTransactionByTypeAxis_5605d569-5c3c-4da2-81f4-d42f7a53d591" xlink:to="loc_kg_RelatedPartyTransactionByTypeDomain_5605d569-5c3c-4da2-81f4-d42f7a53d591_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionByTypeDomain_53223810-31fe-4161-9071-41258f09e4cc" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionByTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_kg_RelatedPartyTransactionByTypeAxis_5605d569-5c3c-4da2-81f4-d42f7a53d591" xlink:to="loc_kg_RelatedPartyTransactionByTypeDomain_53223810-31fe-4161-9071-41258f09e4cc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember_86e338d0-33a1-4b50-b474-fef557af3661" xlink:href="kg-20250930.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RelatedPartyTransactionByTypeDomain_53223810-31fe-4161-9071-41258f09e4cc" xlink:to="loc_kg_AmtrustFinancialServicesIncMember_86e338d0-33a1-4b50-b474-fef557af3661" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentManagementFeesMember_0745c97c-51bb-4294-bea7-10eb9a7e2251" xlink:href="kg-20250930.xsd#kg_InvestmentManagementFeesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_RelatedPartyTransactionByTypeDomain_53223810-31fe-4161-9071-41258f09e4cc" xlink:to="loc_kg_InvestmentManagementFeesMember_0745c97c-51bb-4294-bea7-10eb9a7e2251" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis_6ab5d410-2e96-4740-9962-d3727eed1729" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_us-gaap_DebtInstrumentAxis_6ab5d410-2e96-4740-9962-d3727eed1729" xlink:type="arc" order="12"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_6ab5d410-2e96-4740-9962-d3727eed1729_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DebtInstrumentAxis_6ab5d410-2e96-4740-9962-d3727eed1729" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_6ab5d410-2e96-4740-9962-d3727eed1729_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_c663779e-8f33-4503-99fd-818668ca6bbd" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DebtInstrumentAxis_6ab5d410-2e96-4740-9962-d3727eed1729" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_c663779e-8f33-4503-99fd-818668ca6bbd" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LoanAgreementMember_e8115fe9-48d0-4d4b-8b00-518d09d2df7c" xlink:href="kg-20250930.xsd#kg_LoanAgreementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_c663779e-8f33-4503-99fd-818668ca6bbd" xlink:to="loc_kg_LoanAgreementMember_e8115fe9-48d0-4d4b-8b00-518d09d2df7c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EntitiesOwnedByRelatedPartiesAxis_3ec097d9-04df-4d28-8d2d-81341867663c" xlink:href="kg-20250930.xsd#kg_EntitiesOwnedByRelatedPartiesAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_kg_EntitiesOwnedByRelatedPartiesAxis_3ec097d9-04df-4d28-8d2d-81341867663c" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EntitiesOwnedByRelatedPartiesDomain_3ec097d9-04df-4d28-8d2d-81341867663c_default" xlink:href="kg-20250930.xsd#kg_EntitiesOwnedByRelatedPartiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_kg_EntitiesOwnedByRelatedPartiesAxis_3ec097d9-04df-4d28-8d2d-81341867663c" xlink:to="loc_kg_EntitiesOwnedByRelatedPartiesDomain_3ec097d9-04df-4d28-8d2d-81341867663c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EntitiesOwnedByRelatedPartiesDomain_e479ce70-ea6d-4f14-b527-21a25f024439" xlink:href="kg-20250930.xsd#kg_EntitiesOwnedByRelatedPartiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_kg_EntitiesOwnedByRelatedPartiesAxis_3ec097d9-04df-4d28-8d2d-81341867663c" xlink:to="loc_kg_EntitiesOwnedByRelatedPartiesDomain_e479ce70-ea6d-4f14-b527-21a25f024439" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember_4c838f60-1a58-45a9-9656-ab528e883f2b" xlink:href="kg-20250930.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_EntitiesOwnedByRelatedPartiesDomain_e479ce70-ea6d-4f14-b527-21a25f024439" xlink:to="loc_kg_AmtrustFinancialServicesIncMember_4c838f60-1a58-45a9-9656-ab528e883f2b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentMilestoneTypeAxis_183869dd-55a4-4c08-a601-061fae0548d6" xlink:href="kg-20250930.xsd#kg_InvestmentMilestoneTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1e217d71-b4d5-4007-b2ff-b484fb76cc93" xlink:to="loc_kg_InvestmentMilestoneTypeAxis_183869dd-55a4-4c08-a601-061fae0548d6" xlink:type="arc" order="14"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentMilestoneTypeDomain_183869dd-55a4-4c08-a601-061fae0548d6_default" xlink:href="kg-20250930.xsd#kg_InvestmentMilestoneTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_kg_InvestmentMilestoneTypeAxis_183869dd-55a4-4c08-a601-061fae0548d6" xlink:to="loc_kg_InvestmentMilestoneTypeDomain_183869dd-55a4-4c08-a601-061fae0548d6_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentMilestoneTypeDomain_c07189cc-ec37-437f-a67a-97281baffb96" xlink:href="kg-20250930.xsd#kg_InvestmentMilestoneTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_kg_InvestmentMilestoneTypeAxis_183869dd-55a4-4c08-a601-061fae0548d6" xlink:to="loc_kg_InvestmentMilestoneTypeDomain_c07189cc-ec37-437f-a67a-97281baffb96" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentOwnership25PercentMember_262bc078-7a6e-400a-bc67-09badfeb5223" xlink:href="kg-20250930.xsd#kg_InvestmentOwnership25PercentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_InvestmentMilestoneTypeDomain_c07189cc-ec37-437f-a67a-97281baffb96" xlink:to="loc_kg_InvestmentOwnership25PercentMember_262bc078-7a6e-400a-bc67-09badfeb5223" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentOwnership5PercentMember_77baa098-31b1-4209-a860-0f7636955585" xlink:href="kg-20250930.xsd#kg_InvestmentOwnership5PercentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_InvestmentMilestoneTypeDomain_c07189cc-ec37-437f-a67a-97281baffb96" xlink:to="loc_kg_InvestmentOwnership5PercentMember_77baa098-31b1-4209-a860-0f7636955585" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentOwnershipAtMergerClosingMember_fafffe28-52f5-4a4c-9ef2-6aa523f07c0a" xlink:href="kg-20250930.xsd#kg_InvestmentOwnershipAtMergerClosingMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_kg_InvestmentMilestoneTypeDomain_c07189cc-ec37-437f-a67a-97281baffb96" xlink:to="loc_kg_InvestmentOwnershipAtMergerClosingMember_fafffe28-52f5-4a4c-9ef2-6aa523f07c0a" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ControllingInterestOwnershipPercentage_2c36b208-f3bf-482c-9477-315566ce7d01" xlink:href="kg-20250930.xsd#kg_ControllingInterestOwnershipPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_ControllingInterestOwnershipPercentage_2c36b208-f3bf-482c-9477-315566ce7d01" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_8ea688a7-544d-47b0-8e76-6f9490ef8292" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_8ea688a7-544d-47b0-8e76-6f9490ef8292" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedBalanceShares_cd9b3379-08de-4979-a7b1-c0b3502be05f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedBalanceShares"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_InvestmentOwnedBalanceShares_cd9b3379-08de-4979-a7b1-c0b3502be05f" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage_b3bd0a00-1aa1-4f66-814e-bcab3583a1b7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage_b3bd0a00-1aa1-4f66-814e-bcab3583a1b7" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfNonIndependentDirectors_9f3f5b94-6af0-4a74-ae17-4db486d91f22" xlink:href="kg-20250930.xsd#kg_NumberOfNonIndependentDirectors"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_NumberOfNonIndependentDirectors_9f3f5b94-6af0-4a74-ae17-4db486d91f22" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfIndependentDirectors_d5331c48-500b-40da-814c-96a90d13a797" xlink:href="kg-20250930.xsd#kg_NumberOfIndependentDirectors"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_NumberOfIndependentDirectors_d5331c48-500b-40da-814c-96a90d13a797" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee_a6a89151-eba2-4c6a-b56e-9c22ccaa93bd" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee_a6a89151-eba2-4c6a-b56e-9c22ccaa93bd" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_3195c3e7-a969-4894-af24-64b2887d9ed1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_3195c3e7-a969-4894-af24-64b2887d9ed1" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense_2b25b978-18b8-44a7-892f-95021b96c875" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_GeneralAndAdministrativeExpense_2b25b978-18b8-44a7-892f-95021b96c875" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationAcquisitionOptionTerm_cbf7b5f3-f3fd-44ed-a4c0-06945687dbda" xlink:href="kg-20250930.xsd#kg_BusinessCombinationAcquisitionOptionTerm"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_BusinessCombinationAcquisitionOptionTerm_cbf7b5f3-f3fd-44ed-a4c0-06945687dbda" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfDirectors_7139c14f-a2a5-4f53-968d-eba01406875c" xlink:href="kg-20250930.xsd#kg_NumberOfDirectors"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_NumberOfDirectors_7139c14f-a2a5-4f53-968d-eba01406875c" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfDirectorsSelectedByAffiliate_19669863-f27e-4b32-ad41-94e05c6a0ff1" xlink:href="kg-20250930.xsd#kg_NumberOfDirectorsSelectedByAffiliate"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_NumberOfDirectorsSelectedByAffiliate_19669863-f27e-4b32-ad41-94e05c6a0ff1" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty_69de8826-994f-4c90-9526-2e9bffb21cf2" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty_69de8826-994f-4c90-9526-2e9bffb21cf2" xlink:type="arc" order="12"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty_0d99e0ae-3701-44fa-9a6d-eaa9c4707c4f" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty_0d99e0ae-3701-44fa-9a6d-eaa9c4707c4f" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums_368c21c7-33e7-4e5e-b520-698a88cd5e14" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums_368c21c7-33e7-4e5e-b520-698a88cd5e14" xlink:type="arc" order="14"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfCededBusinessAmount_c6432dbd-7168-4253-a4ac-db45554787a4" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionPercentOfCededBusinessAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionPercentOfCededBusinessAmount_c6432dbd-7168-4253-a4ac-db45554787a4" xlink:type="arc" order="15"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor_b49a6b16-8151-4e97-b455-7c02dc57fc2e" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor_b49a6b16-8151-4e97-b455-7c02dc57fc2e" xlink:type="arc" order="16"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling_670b94dd-3933-45bd-8c30-4b606961573d" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling_670b94dd-3933-45bd-8c30-4b606961573d" xlink:type="arc" order="17"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction_85f7a407-787c-4a94-bd9c-2df81d403655" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction_85f7a407-787c-4a94-bd9c-2df81d403655" xlink:type="arc" order="18"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease_ee99c300-b042-4265-9593-b27a87d23213" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease_ee99c300-b042-4265-9593-b27a87d23213" xlink:type="arc" order="19"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies_3425505c-699d-48a5-8e48-70bb10c4bc48" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies_3425505c-699d-48a5-8e48-70bb10c4bc48" xlink:type="arc" order="20"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching_af22810a-c56a-4543-90c0-23369404b9b0" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching_af22810a-c56a-4543-90c0-23369404b9b0" xlink:type="arc" order="21"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching_018e6d4b-acf8-4818-841d-e23d1b101f7f" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching_018e6d4b-acf8-4818-841d-e23d1b101f7f" xlink:type="arc" order="22"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies_4a6c7ad9-7c54-479e-9a4a-e7120ddf491a" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies_4a6c7ad9-7c54-479e-9a4a-e7120ddf491a" xlink:type="arc" order="23"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CollaborativeArrangementPaymentOfCommutedReserves_1f67e0a4-9914-4e97-a104-8ddf6ac6ba7f" xlink:href="kg-20250930.xsd#kg_CollaborativeArrangementPaymentOfCommutedReserves"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_CollaborativeArrangementPaymentOfCommutedReserves_1f67e0a4-9914-4e97-a104-8ddf6ac6ba7f" xlink:type="arc" order="24"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CollaborativeArrangementReservesExpectedToBeCommuted_f8887907-73a5-4df7-9ed4-4c869907e022" xlink:href="kg-20250930.xsd#kg_CollaborativeArrangementReservesExpectedToBeCommuted"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_CollaborativeArrangementReservesExpectedToBeCommuted_f8887907-73a5-4df7-9ed4-4c869907e022" xlink:type="arc" order="25"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost_25e15397-b595-4c32-833f-c14e0bab9727" xlink:href="kg-20250930.xsd#kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost_25e15397-b595-4c32-833f-c14e0bab9727" xlink:type="arc" order="26"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations_0f9de525-5daf-47bb-9f86-b268bbc570ad" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations_0f9de525-5daf-47bb-9f86-b268bbc570ad" xlink:type="arc" order="27"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionLoanAgreementObligationThreshold_a7d81b3f-71c8-4817-bc17-9fc75251ddd2" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionLoanAgreementObligationThreshold"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionLoanAgreementObligationThreshold_a7d81b3f-71c8-4817-bc17-9fc75251ddd2" xlink:type="arc" order="28"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionSolvencyRatio_6dc0e4b9-1221-4228-89d6-ba6750c79f78" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionSolvencyRatio"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionSolvencyRatio_6dc0e4b9-1221-4228-89d6-ba6750c79f78" xlink:type="arc" order="29"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure_9877d6d2-dbd4-4605-b58c-61b8f46182e8" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionPercentageOfCollateralOnExposure"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure_9877d6d2-dbd4-4605-b58c-61b8f46182e8" xlink:type="arc" order="30"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayable_add3739d-9df1-496c-b9db-8d5436e3b063" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansPayable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_LoansPayable_add3739d-9df1-496c-b9db-8d5436e3b063" xlink:type="arc" order="31"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_e4aa0f8d-ea1e-46f1-881b-2e415e1898b9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_e4aa0f8d-ea1e-46f1-881b-2e415e1898b9" xlink:type="arc" order="32"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount_1fae9f98-3956-4caf-b4ba-74760853c53d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_DebtInstrumentFaceAmount_1fae9f98-3956-4caf-b4ba-74760853c53d" xlink:type="arc" order="33"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableRelatedParties_8c55d9dc-1947-4595-8199-fe6f52b9752d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableRelatedParties"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_LoansAndLeasesReceivableRelatedParties_8c55d9dc-1947-4595-8199-fe6f52b9752d" xlink:type="arc" order="34"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal_180a98b0-e613-4bbe-8b07-7df2bbcac3ae" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal_180a98b0-e613-4bbe-8b07-7df2bbcac3ae" xlink:type="arc" order="35"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterestAndDividend_5c124a68-c9a5-4f51-ad07-5e03faefe5d7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInterestAndDividend"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_InvestmentIncomeInterestAndDividend_5c124a68-c9a5-4f51-ad07-5e03faefe5d7" xlink:type="arc" order="36"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate_c0386e7f-c54a-49eb-b3c5-3490a6c1d12a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate_c0386e7f-c54a-49eb-b3c5-3490a6c1d12a" xlink:type="arc" order="37"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCollateralHeldByRelatedParty_8271ee62-265a-4131-a04c-8b1b8b67ccee" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionCollateralHeldByRelatedParty"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionCollateralHeldByRelatedParty_8271ee62-265a-4131-a04c-8b1b8b67ccee" xlink:type="arc" order="38"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty_57121b5e-f81b-4102-9d02-ef288e26d9de" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty_57121b5e-f81b-4102-9d02-ef288e26d9de" xlink:type="arc" order="39"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings_d41dc0f2-17f6-4a16-9275-de26170c0bf5" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings_d41dc0f2-17f6-4a16-9275-de26170c0bf5" xlink:type="arc" order="40"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCancellationNoticePeriod_0d575b59-eda8-4ed2-be6b-52332d02e817" xlink:href="kg-20250930.xsd#kg_RelatedPartyTransactionCancellationNoticePeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_kg_RelatedPartyTransactionCancellationNoticePeriod_0d575b59-eda8-4ed2-be6b-52332d02e817" xlink:type="arc" order="41"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementFeeExpense_8564231c-3b65-48d1-81fb-aa79a11496c5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ManagementFeeExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_cb29bb9e-4faf-4c07-9b00-7d6a25070cd7" xlink:to="loc_us-gaap_ManagementFeeExpense_8564231c-3b65-48d1-81fb-aa79a11496c5" xlink:type="arc" order="42"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/RelatedPartyTransactionsScheduleofQuotaShareArrangementswithAmTrustDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#RelatedPartyTransactionsScheduleofQuotaShareArrangementswithAmTrustDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/RelatedPartyTransactionsScheduleofQuotaShareArrangementswithAmTrustDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems_a317493f-25f9-432a-b5d2-ffe0c5547261" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_895c8a2e-3902-46db-b6c6-06826048e167" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_a317493f-25f9-432a-b5d2-ffe0c5547261" xlink:to="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_895c8a2e-3902-46db-b6c6-06826048e167" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TypeOfArrangementAxis_f94de02c-83c8-4d42-a6fe-587de5a27d87" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfArrangementAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_895c8a2e-3902-46db-b6c6-06826048e167" xlink:to="loc_us-gaap_TypeOfArrangementAxis_f94de02c-83c8-4d42-a6fe-587de5a27d87" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_f94de02c-83c8-4d42-a6fe-587de5a27d87_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_TypeOfArrangementAxis_f94de02c-83c8-4d42-a6fe-587de5a27d87" xlink:to="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_f94de02c-83c8-4d42-a6fe-587de5a27d87_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_accd9463-2de9-4f8f-8df3-3fe5dce7b220" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_TypeOfArrangementAxis_f94de02c-83c8-4d42-a6fe-587de5a27d87" xlink:to="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_accd9463-2de9-4f8f-8df3-3fe5dce7b220" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_QuotaShareReinsuranceAgreementsMember_54496bdc-c7ca-457f-88b1-777ad802b974" xlink:href="kg-20250930.xsd#kg_QuotaShareReinsuranceAgreementsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember_accd9463-2de9-4f8f-8df3-3fe5dce7b220" xlink:to="loc_kg_QuotaShareReinsuranceAgreementsMember_54496bdc-c7ca-457f-88b1-777ad802b974" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_7b463af0-6eaf-42d1-809f-33653430d66f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_895c8a2e-3902-46db-b6c6-06826048e167" xlink:to="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_7b463af0-6eaf-42d1-809f-33653430d66f" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_7b463af0-6eaf-42d1-809f-33653430d66f_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_7b463af0-6eaf-42d1-809f-33653430d66f" xlink:to="loc_us-gaap_RelatedPartyDomain_7b463af0-6eaf-42d1-809f-33653430d66f_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_abd08389-7738-46b3-9ff7-f298c84f78b4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_7b463af0-6eaf-42d1-809f-33653430d66f" xlink:to="loc_us-gaap_RelatedPartyDomain_abd08389-7738-46b3-9ff7-f298c84f78b4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember_d02d4d1d-5a39-4be7-8fae-5b1a1f52ed9d" xlink:href="kg-20250930.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyDomain_abd08389-7738-46b3-9ff7-f298c84f78b4" xlink:to="loc_kg_AmtrustFinancialServicesIncMember_d02d4d1d-5a39-4be7-8fae-5b1a1f52ed9d" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PremiumWrittenGrossAndNet_aca89463-66c0-4d8c-bc51-62d179be9a82" xlink:href="kg-20250930.xsd#kg_PremiumWrittenGrossAndNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_a317493f-25f9-432a-b5d2-ffe0c5547261" xlink:to="loc_kg_PremiumWrittenGrossAndNet_aca89463-66c0-4d8c-bc51-62d179be9a82" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsEarnedNet_c5943619-a498-4746-960e-d89afcf161ab" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsEarnedNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_a317493f-25f9-432a-b5d2-ffe0c5547261" xlink:to="loc_us-gaap_PremiumsEarnedNet_c5943619-a498-4746-960e-d89afcf161ab" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_d8f0fa1c-e2a0-4e16-83dd-c6f53dfd3705" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_a317493f-25f9-432a-b5d2-ffe0c5547261" xlink:to="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_d8f0fa1c-e2a0-4e16-83dd-c6f53dfd3705" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_8b2002ab-01e1-43dc-b453-5649da3b2f8a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_a317493f-25f9-432a-b5d2-ffe0c5547261" xlink:to="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_8b2002ab-01e1-43dc-b453-5649da3b2f8a" xlink:type="arc" order="3"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/CommitmentsContingenciesandGuaranteesNarrativeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#CommitmentsContingenciesandGuaranteesNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/CommitmentsContingenciesandGuaranteesNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainContingenciesLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainContingenciesTable_f0c4a526-132b-4f8c-8d0f-1512757fbc48" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainContingenciesTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_GainContingenciesTable_f0c4a526-132b-4f8c-8d0f-1512757fbc48" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_c5b50a68-f161-4b07-a28a-a9b6f7004270" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_GainContingenciesTable_f0c4a526-132b-4f8c-8d0f-1512757fbc48" xlink:to="loc_us-gaap_FinancialInstrumentAxis_c5b50a68-f161-4b07-a28a-a9b6f7004270" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_c5b50a68-f161-4b07-a28a-a9b6f7004270_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_c5b50a68-f161-4b07-a28a-a9b6f7004270" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_c5b50a68-f161-4b07-a28a-a9b6f7004270_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4f09037d-eb7a-43f3-be46-0884ecae91d5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_c5b50a68-f161-4b07-a28a-a9b6f7004270" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4f09037d-eb7a-43f3-be46-0884ecae91d5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_26d09318-7b25-4c40-894b-931a72cd592b" xlink:href="kg-20250930.xsd#kg_OtherInvestmentsAndEquityMethodInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_4f09037d-eb7a-43f3-be46-0884ecae91d5" xlink:to="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_26d09318-7b25-4c40-894b-931a72cd592b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_753420fc-09a5-4ede-87d5-154a003af45d" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_GainContingenciesTable_f0c4a526-132b-4f8c-8d0f-1512757fbc48" xlink:to="loc_srt_RangeAxis_753420fc-09a5-4ede-87d5-154a003af45d" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_753420fc-09a5-4ede-87d5-154a003af45d_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_753420fc-09a5-4ede-87d5-154a003af45d" xlink:to="loc_srt_RangeMember_753420fc-09a5-4ede-87d5-154a003af45d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_040b6b64-bb5e-4643-94e6-ac2863b4bb03" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_753420fc-09a5-4ede-87d5-154a003af45d" xlink:to="loc_srt_RangeMember_040b6b64-bb5e-4643-94e6-ac2863b4bb03" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember_4d63b1fe-2622-404b-a96b-b001a9ffa6c3" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_040b6b64-bb5e-4643-94e6-ac2863b4bb03" xlink:to="loc_srt_MinimumMember_4d63b1fe-2622-404b-a96b-b001a9ffa6c3" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_b120b6c5-036c-4f5a-983a-b0a9ca9680c3" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_040b6b64-bb5e-4643-94e6-ac2863b4bb03" xlink:to="loc_srt_MaximumMember_b120b6c5-036c-4f5a-983a-b0a9ca9680c3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis_89df4272-db5e-4fe1-96a6-c02b68c31a80" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_GainContingenciesTable_f0c4a526-132b-4f8c-8d0f-1512757fbc48" xlink:to="loc_us-gaap_BusinessAcquisitionAxis_89df4272-db5e-4fe1-96a6-c02b68c31a80" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_89df4272-db5e-4fe1-96a6-c02b68c31a80_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_89df4272-db5e-4fe1-96a6-c02b68c31a80" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_89df4272-db5e-4fe1-96a6-c02b68c31a80_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_0887a18b-cc8a-4b9a-a92b-677285c2a11d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_89df4272-db5e-4fe1-96a6-c02b68c31a80" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_0887a18b-cc8a-4b9a-a92b-677285c2a11d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_30782766-ba81-4ab5-ad04-38ea1ed84bb1" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain_0887a18b-cc8a-4b9a-a92b-677285c2a11d" xlink:to="loc_kg_KestrelGroupLtd.Member_30782766-ba81-4ab5-ad04-38ea1ed84bb1" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_bd7b44b6-0c22-4daa-a90f-e49efc94ae4c" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_GainContingenciesTable_f0c4a526-132b-4f8c-8d0f-1512757fbc48" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_bd7b44b6-0c22-4daa-a90f-e49efc94ae4c" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_bd7b44b6-0c22-4daa-a90f-e49efc94ae4c_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_bd7b44b6-0c22-4daa-a90f-e49efc94ae4c" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_bd7b44b6-0c22-4daa-a90f-e49efc94ae4c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_7785ab0a-8a9f-4960-8a79-ff44e5571404" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_bd7b44b6-0c22-4daa-a90f-e49efc94ae4c" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_7785ab0a-8a9f-4960-8a79-ff44e5571404" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetPurchaseAgreementMember_b320629a-64b5-40ba-989c-d6719f237a44" xlink:href="kg-20250930.xsd#kg_AssetPurchaseAgreementMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_7785ab0a-8a9f-4960-8a79-ff44e5571404" xlink:to="loc_kg_AssetPurchaseAgreementMember_b320629a-64b5-40ba-989c-d6719f237a44" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments_89740799-8b79-43ea-b7dc-7e1462e801c0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments_89740799-8b79-43ea-b7dc-7e1462e801c0" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeExtensibleEnumeration_5b72e294-31de-4179-8f8a-2926168190a9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeExtensibleEnumeration"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments_89740799-8b79-43ea-b7dc-7e1462e801c0" xlink:to="loc_us-gaap_InvestmentTypeExtensibleEnumeration_5b72e294-31de-4179-8f8a-2926168190a9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitment_82092edb-7674-4210-a685-9c666ff3eebc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_OtherCommitment_82092edb-7674-4210-a685-9c666ff3eebc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiability_26196d76-77ab-4896-9224-847d8666f190" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_BusinessCombinationContingentConsiderationLiability_26196d76-77ab-4896-9224-847d8666f190" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_b09cb231-5ebb-4b2f-a27e-e89701c92fd1" xlink:href="kg-20250930.xsd#kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_b09cb231-5ebb-4b2f-a27e-e89701c92fd1" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_dbe17381-3edc-41fe-adf4-fa8779dc9e80" xlink:href="kg-20250930.xsd#kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_dbe17381-3edc-41fe-adf4-fa8779dc9e80" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsDistributionsNetPresentValue_0b8f1df4-e2ca-4191-b0e2-24bc90d89134" xlink:href="kg-20250930.xsd#kg_EquityMethodInvestmentsDistributionsNetPresentValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_kg_EquityMethodInvestmentsDistributionsNetPresentValue_0b8f1df4-e2ca-4191-b0e2-24bc90d89134" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OperatingLeaseEscalatingFeePercentage_3d8ace02-fb97-4146-9180-e5ecd219d511" xlink:href="kg-20250930.xsd#kg_OperatingLeaseEscalatingFeePercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_kg_OperatingLeaseEscalatingFeePercentage_3d8ace02-fb97-4146-9180-e5ecd219d511" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseTermOfContract_c0719ead-9087-4901-bec7-1a3b6c02be2b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseTermOfContract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_LesseeOperatingLeaseTermOfContract_c0719ead-9087-4901-bec7-1a3b6c02be2b" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_e6aeda32-7c2d-4d8e-a5be-063526caaf2a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_e6aeda32-7c2d-4d8e-a5be-063526caaf2a" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability_7a238592-96ed-458e-9ec8-6339e719efe3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_OperatingLeaseLiability_7a238592-96ed-458e-9ec8-6339e719efe3" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_a078052c-2fb8-4ab9-abf0-96c55a6dc981" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_a078052c-2fb8-4ab9-abf0-96c55a6dc981" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_1679d4aa-264c-4cf4-ae80-f0eb781b05fd" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_1679d4aa-264c-4cf4-ae80-f0eb781b05fd" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset_b651d45d-c1e1-415d-b46d-1082c97720c3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_OperatingLeaseRightOfUseAsset_b651d45d-c1e1-415d-b46d-1082c97720c3" xlink:type="arc" order="12"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_c32ff690-9cd6-4aac-9261-3d0547470efa" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_c32ff690-9cd6-4aac-9261-3d0547470efa" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseExpense_9605fc1a-f1b1-4985-aa25-14ddeec36994" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_us-gaap_OperatingLeaseExpense_9605fc1a-f1b1-4985-aa25-14ddeec36994" xlink:type="arc" order="14"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit_c62bc53f-ab47-483a-90b2-0a7f1bb83bed" xlink:href="kg-20250930.xsd#kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_466f0fd0-1986-4217-ba8f-080440296290" xlink:to="loc_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit_c62bc53f-ab47-483a-90b2-0a7f1bb83bed" xlink:type="arc" order="15"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/CommitmentsContingenciesandGuaranteesScheduleofTotalUnfundedCommitmentsDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#CommitmentsContingenciesandGuaranteesScheduleofTotalUnfundedCommitmentsDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/CommitmentsContingenciesandGuaranteesScheduleofTotalUnfundedCommitmentsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainContingenciesLineItems_758f9fab-72cc-4efa-9bed-3b7d501233a3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainContingenciesLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainContingenciesTable_154e37a1-fb17-44a7-9825-fc54067fd1b1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainContingenciesTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_GainContingenciesLineItems_758f9fab-72cc-4efa-9bed-3b7d501233a3" xlink:to="loc_us-gaap_GainContingenciesTable_154e37a1-fb17-44a7-9825-fc54067fd1b1" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_f951cbb4-55e1-4201-9ca3-714884ce19e3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_GainContingenciesTable_154e37a1-fb17-44a7-9825-fc54067fd1b1" xlink:to="loc_us-gaap_FinancialInstrumentAxis_f951cbb4-55e1-4201-9ca3-714884ce19e3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_f951cbb4-55e1-4201-9ca3-714884ce19e3_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_f951cbb4-55e1-4201-9ca3-714884ce19e3" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_f951cbb4-55e1-4201-9ca3-714884ce19e3_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_6b67608d-b8cb-40ea-8a73-56896e72f0e6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_f951cbb4-55e1-4201-9ca3-714884ce19e3" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_6b67608d-b8cb-40ea-8a73-56896e72f0e6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestmentsMember_94dcccb0-51e6-47bf-973a-5d8effe832cb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_6b67608d-b8cb-40ea-8a73-56896e72f0e6" xlink:to="loc_us-gaap_OtherInvestmentsMember_94dcccb0-51e6-47bf-973a-5d8effe832cb" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsMember_2555204e-6917-4979-8d6e-20ff62331e62" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_6b67608d-b8cb-40ea-8a73-56896e72f0e6" xlink:to="loc_us-gaap_EquityMethodInvestmentsMember_2555204e-6917-4979-8d6e-20ff62331e62" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_52b49eab-e027-4378-933b-d85e87844281" xlink:href="kg-20250930.xsd#kg_OtherInvestmentsAndEquityMethodInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_6b67608d-b8cb-40ea-8a73-56896e72f0e6" xlink:to="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_52b49eab-e027-4378-933b-d85e87844281" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments_efbdf7cb-5e35-46fc-b776-89c496d6772d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_758f9fab-72cc-4efa-9bed-3b7d501233a3" xlink:to="loc_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments_efbdf7cb-5e35-46fc-b776-89c496d6772d" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal_8a11da34-258f-4ebd-bd71-256d1dc85149" xlink:href="kg-20250930.xsd#kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_GainContingenciesLineItems_758f9fab-72cc-4efa-9bed-3b7d501233a3" xlink:to="loc_kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal_8a11da34-258f-4ebd-bd71-256d1dc85149" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/IncomeTaxesDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#IncomeTaxesDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/IncomeTaxesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsLineItems_c12f5ea0-ba55-40c5-b2f8-1d4954f7d48c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwardsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsTable_e121ea83-093a-4a5b-9721-bf3f644b594d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwardsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_OperatingLossCarryforwardsLineItems_c12f5ea0-ba55-40c5-b2f8-1d4954f7d48c" xlink:to="loc_us-gaap_OperatingLossCarryforwardsTable_e121ea83-093a-4a5b-9721-bf3f644b594d" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityAxis_5ff33adc-9ef3-4aa0-bb49-33dfa5f75cdc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_OperatingLossCarryforwardsTable_e121ea83-093a-4a5b-9721-bf3f644b594d" xlink:to="loc_us-gaap_IncomeTaxAuthorityAxis_5ff33adc-9ef3-4aa0-bb49-33dfa5f75cdc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain_5ff33adc-9ef3-4aa0-bb49-33dfa5f75cdc_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_IncomeTaxAuthorityAxis_5ff33adc-9ef3-4aa0-bb49-33dfa5f75cdc" xlink:to="loc_us-gaap_IncomeTaxAuthorityDomain_5ff33adc-9ef3-4aa0-bb49-33dfa5f75cdc_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain_acc4a3fc-ed23-43d2-b937-223d8cf9b54f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_IncomeTaxAuthorityAxis_5ff33adc-9ef3-4aa0-bb49-33dfa5f75cdc" xlink:to="loc_us-gaap_IncomeTaxAuthorityDomain_acc4a3fc-ed23-43d2-b937-223d8cf9b54f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalRevenueServiceIRSMember_86e63b95-b4f8-46e6-b09f-eb77615da747" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InternalRevenueServiceIRSMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeTaxAuthorityDomain_acc4a3fc-ed23-43d2-b937-223d8cf9b54f" xlink:to="loc_us-gaap_InternalRevenueServiceIRSMember_86e63b95-b4f8-46e6-b09f-eb77615da747" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit_e236bb4c-1ff1-405f-ae71-82eb64f6a67e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OperatingLossCarryforwardsLineItems_c12f5ea0-ba55-40c5-b2f8-1d4954f7d48c" xlink:to="loc_us-gaap_IncomeTaxExpenseBenefit_e236bb4c-1ff1-405f-ae71-82eb64f6a67e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwards_2a772f74-253e-4230-a43b-214b8b37f033" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwards"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OperatingLossCarryforwardsLineItems_c12f5ea0-ba55-40c5-b2f8-1d4954f7d48c" xlink:to="loc_us-gaap_OperatingLossCarryforwards_2a772f74-253e-4230-a43b-214b8b37f033" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_3efc6f96-2c9e-4920-a8cc-18d93fb91090" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OperatingLossCarryforwardsLineItems_c12f5ea0-ba55-40c5-b2f8-1d4954f7d48c" xlink:to="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_3efc6f96-2c9e-4920-a8cc-18d93fb91090" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration_27f0d918-aa27-454d-8f60-abcab3cac3e6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OperatingLossCarryforwardsLineItems_c12f5ea0-ba55-40c5-b2f8-1d4954f7d48c" xlink:to="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration_27f0d918-aa27-454d-8f60-abcab3cac3e6" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage_9d4b0de4-4663-4d3b-b918-af96cbf2cf11" xlink:href="kg-20250930.xsd#kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OperatingLossCarryforwardsLineItems_c12f5ea0-ba55-40c5-b2f8-1d4954f7d48c" xlink:to="loc_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage_9d4b0de4-4663-4d3b-b918-af96cbf2cf11" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/AssetsHeldforSaleScheduleofAssetsandLiabilitiesClassifiedasHeldforSaleDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#AssetsHeldforSaleScheduleofAssetsandLiabilitiesClassifiedasHeldforSaleDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/AssetsHeldforSaleScheduleofAssetsandLiabilitiesClassifiedasHeldforSaleDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_f5558dfe-55cd-4d7c-a509-9cf957688a89" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_2205a87e-8115-431d-978d-864965f098dd" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_f5558dfe-55cd-4d7c-a509-9cf957688a89" xlink:to="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_2205a87e-8115-431d-978d-864965f098dd" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationAxis_2a499a2d-f544-4979-8238-4802732c7c57" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_2205a87e-8115-431d-978d-864965f098dd" xlink:to="loc_us-gaap_DisposalGroupClassificationAxis_2a499a2d-f544-4979-8238-4802732c7c57" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationDomain_2a499a2d-f544-4979-8238-4802732c7c57_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis_2a499a2d-f544-4979-8238-4802732c7c57" xlink:to="loc_us-gaap_DisposalGroupClassificationDomain_2a499a2d-f544-4979-8238-4802732c7c57_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationDomain_1761c251-bfdb-4025-ace5-dfd816f1c070" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis_2a499a2d-f544-4979-8238-4802732c7c57" xlink:to="loc_us-gaap_DisposalGroupClassificationDomain_1761c251-bfdb-4025-ace5-dfd816f1c070" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsHeldforsaleMember_7fdb27ee-99cc-411c-9b65-f6e4af41b623" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationsHeldforsaleMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DisposalGroupClassificationDomain_1761c251-bfdb-4025-ace5-dfd816f1c070" xlink:to="loc_us-gaap_DiscontinuedOperationsHeldforsaleMember_7fdb27ee-99cc-411c-9b65-f6e4af41b623" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_6b4c274c-6237-4fd5-bd44-158317d06fd2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_f5558dfe-55cd-4d7c-a509-9cf957688a89" xlink:to="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_6b4c274c-6237-4fd5-bd44-158317d06fd2" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities_bf6e692d-0eb8-4b41-947b-2823a6c6cd5a" xlink:href="kg-20250930.xsd#kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_6b4c274c-6237-4fd5-bd44-158317d06fd2" xlink:to="loc_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities_bf6e692d-0eb8-4b41-947b-2823a6c6cd5a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_cad031c5-42c7-43b9-be76-0b9fa2a726f1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_6b4c274c-6237-4fd5-bd44-158317d06fd2" xlink:to="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_cad031c5-42c7-43b9-be76-0b9fa2a726f1" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome_e54c00b0-b356-4245-969b-0c15e839a33e" xlink:href="kg-20250930.xsd#kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_6b4c274c-6237-4fd5-bd44-158317d06fd2" xlink:to="loc_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome_e54c00b0-b356-4245-969b-0c15e839a33e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets_fb441833-d8b6-4ae2-8901-d8d3b7c3156f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_6b4c274c-6237-4fd5-bd44-158317d06fd2" xlink:to="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets_fb441833-d8b6-4ae2-8901-d8d3b7c3156f" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_dc4432c3-c858-4bfc-818e-da4b4b279879" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_6b4c274c-6237-4fd5-bd44-158317d06fd2" xlink:to="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_dc4432c3-c858-4bfc-818e-da4b4b279879" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_4984243d-e9df-482d-936e-2b8adeb8d8b8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_f5558dfe-55cd-4d7c-a509-9cf957688a89" xlink:to="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_4984243d-e9df-482d-936e-2b8adeb8d8b8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities_75bc3813-8790-4674-999f-3397a2ed383f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_4984243d-e9df-482d-936e-2b8adeb8d8b8" xlink:to="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities_75bc3813-8790-4674-999f-3397a2ed383f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_00c77f2d-22fd-4da8-ac39-b406e81edf11" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_4984243d-e9df-482d-936e-2b8adeb8d8b8" xlink:to="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_00c77f2d-22fd-4da8-ac39-b406e81edf11" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/AssetsHeldforSaleScheduleofIncomeStatementDisclosuresDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#AssetsHeldforSaleScheduleofIncomeStatementDisclosuresDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/AssetsHeldforSaleScheduleofIncomeStatementDisclosuresDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_44c8fcd9-7413-4940-9eab-3149f224efe6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_074ddc09-78b0-40ed-b884-f3835c4be152" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_44c8fcd9-7413-4940-9eab-3149f224efe6" xlink:to="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_074ddc09-78b0-40ed-b884-f3835c4be152" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationAxis_df5ea041-35d6-444d-a8e8-3d2fa5560029" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_074ddc09-78b0-40ed-b884-f3835c4be152" xlink:to="loc_us-gaap_DisposalGroupClassificationAxis_df5ea041-35d6-444d-a8e8-3d2fa5560029" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationDomain_df5ea041-35d6-444d-a8e8-3d2fa5560029_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis_df5ea041-35d6-444d-a8e8-3d2fa5560029" xlink:to="loc_us-gaap_DisposalGroupClassificationDomain_df5ea041-35d6-444d-a8e8-3d2fa5560029_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationDomain_9ad9c2f2-fcac-4be3-80f6-6e7e1bdd3a72" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis_df5ea041-35d6-444d-a8e8-3d2fa5560029" xlink:to="loc_us-gaap_DisposalGroupClassificationDomain_9ad9c2f2-fcac-4be3-80f6-6e7e1bdd3a72" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsHeldforsaleMember_ba694c4c-5bf1-42a8-972e-5af3714ba511" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationsHeldforsaleMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DisposalGroupClassificationDomain_9ad9c2f2-fcac-4be3-80f6-6e7e1bdd3a72" xlink:to="loc_us-gaap_DiscontinuedOperationsHeldforsaleMember_ba694c4c-5bf1-42a8-972e-5af3714ba511" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet_8bffeb8e-0a62-4f6e-bb27-02c9e23f2ba8" xlink:href="kg-20250930.xsd#kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_44c8fcd9-7413-4940-9eab-3149f224efe6" xlink:to="loc_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet_8bffeb8e-0a62-4f6e-bb27-02c9e23f2ba8" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense_01915ad7-8640-4314-9511-49cc76222def" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_44c8fcd9-7413-4940-9eab-3149f224efe6" xlink:to="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense_01915ad7-8640-4314-9511-49cc76222def" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses_98ea2d96-3cb7-48f9-85c1-d75788f86820" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_44c8fcd9-7413-4940-9eab-3149f224efe6" xlink:to="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses_98ea2d96-3cb7-48f9-85c1-d75788f86820" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_9e726d2b-b47a-4669-bcf4-8b4bd664392e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_44c8fcd9-7413-4940-9eab-3149f224efe6" xlink:to="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_9e726d2b-b47a-4669-bcf4-8b4bd664392e" xlink:type="arc" order="3"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/BusinessCombinationNarrativeDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#BusinessCombinationNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/BusinessCombinationNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_ea2931ab-5faa-480c-ba14-2d56e9adede5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_ea2931ab-5faa-480c-ba14-2d56e9adede5" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis_75c36686-2e23-4cad-8cfc-d337199dbed0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_ea2931ab-5faa-480c-ba14-2d56e9adede5" xlink:to="loc_us-gaap_BusinessAcquisitionAxis_75c36686-2e23-4cad-8cfc-d337199dbed0" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_75c36686-2e23-4cad-8cfc-d337199dbed0_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_75c36686-2e23-4cad-8cfc-d337199dbed0" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_75c36686-2e23-4cad-8cfc-d337199dbed0_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_aa21a315-4c01-43cc-8ec0-1c0c6c513333" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_75c36686-2e23-4cad-8cfc-d337199dbed0" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_aa21a315-4c01-43cc-8ec0-1c0c6c513333" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_3696c653-5710-4379-9e0c-d2fdb0083a40" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain_aa21a315-4c01-43cc-8ec0-1c0c6c513333" xlink:to="loc_kg_KestrelGroupLtd.Member_3696c653-5710-4379-9e0c-d2fdb0083a40" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_ed41a936-1b29-49fc-8800-6c76646a2562" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_ea2931ab-5faa-480c-ba14-2d56e9adede5" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_ed41a936-1b29-49fc-8800-6c76646a2562" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_ed41a936-1b29-49fc-8800-6c76646a2562_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_ed41a936-1b29-49fc-8800-6c76646a2562" xlink:to="loc_us-gaap_EquityComponentDomain_ed41a936-1b29-49fc-8800-6c76646a2562_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_2e4f957c-0447-4bfe-862b-74424b362b2b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_ed41a936-1b29-49fc-8800-6c76646a2562" xlink:to="loc_us-gaap_EquityComponentDomain_2e4f957c-0447-4bfe-862b-74424b362b2b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_9bd2cbc3-a30c-4f27-bb39-3efdb62181f7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_2e4f957c-0447-4bfe-862b-74424b362b2b" xlink:to="loc_us-gaap_CommonStockMember_9bd2cbc3-a30c-4f27-bb39-3efdb62181f7" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross_40e3cc08-57bf-46ac-bac1-f43f0099b95a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_us-gaap_PaymentsToAcquireBusinessesGross_40e3cc08-57bf-46ac-bac1-f43f0099b95a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_93e7a36e-e355-414f-a9a4-472e67e22e04" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_93e7a36e-e355-414f-a9a4-472e67e22e04" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiability_5fa1f50f-ea27-47d4-8a83-8e405425080d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_us-gaap_BusinessCombinationContingentConsiderationLiability_5fa1f50f-ea27-47d4-8a83-8e405425080d" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_d4468713-1e30-4b71-ac50-62da8cf5a358" xlink:href="kg-20250930.xsd#kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_d4468713-1e30-4b71-ac50-62da8cf5a358" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized_86a4002c-b663-465f-afd7-cfffa7066789" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_us-gaap_CommonStockSharesAuthorized_86a4002c-b663-465f-afd7-cfffa7066789" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_364cdf24-bb0b-49b2-9acf-41f4eaacd36f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_364cdf24-bb0b-49b2-9acf-41f4eaacd36f" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferred1_5cd5cc6b-a25d-4aab-91c3-77a873fd1327" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferred1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_us-gaap_BusinessCombinationConsiderationTransferred1_5cd5cc6b-a25d-4aab-91c3-77a873fd1327" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_6917329f-bfc8-4eef-98f4-7a18bdac6423" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_6917329f-bfc8-4eef-98f4-7a18bdac6423" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_57b56e8c-1797-462b-8d01-1da6d20cc622" xlink:href="kg-20250930.xsd#kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_7b971c2a-4a5c-4b99-a871-beac19057ddb" xlink:to="loc_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_57b56e8c-1797-462b-8d01-1da6d20cc622" xlink:type="arc" order="8"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/BusinessCombinationScheduleofPurchasePriceDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#BusinessCombinationScheduleofPurchasePriceDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/BusinessCombinationScheduleofPurchasePriceDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_4b52e0cf-901b-4776-a1e7-1bfb4a4547e9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_4b52e0cf-901b-4776-a1e7-1bfb4a4547e9" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis_e897b2ac-7060-4294-97b9-c0bdb10ed3c4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_4b52e0cf-901b-4776-a1e7-1bfb4a4547e9" xlink:to="loc_us-gaap_BusinessAcquisitionAxis_e897b2ac-7060-4294-97b9-c0bdb10ed3c4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_e897b2ac-7060-4294-97b9-c0bdb10ed3c4_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_e897b2ac-7060-4294-97b9-c0bdb10ed3c4" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_e897b2ac-7060-4294-97b9-c0bdb10ed3c4_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_5f780634-9377-4ae1-b391-b9d1637daf2b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_e897b2ac-7060-4294-97b9-c0bdb10ed3c4" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_5f780634-9377-4ae1-b391-b9d1637daf2b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_f9d2e3fb-09f7-43cc-8ba2-04e5f2136bd0" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain_5f780634-9377-4ae1-b391-b9d1637daf2b" xlink:to="loc_kg_KestrelGroupLtd.Member_f9d2e3fb-09f7-43cc-8ba2-04e5f2136bd0" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_2027deb8-1eb1-48a2-8ac5-e53e952126c9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_2027deb8-1eb1-48a2-8ac5-e53e952126c9" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionSharePrice_9653ddcb-b6eb-4961-bc78-49ddad873e3c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionSharePrice"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_us-gaap_BusinessAcquisitionSharePrice_9653ddcb-b6eb-4961-bc78-49ddad873e3c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock_06d31e02-8e7e-42d3-8d54-9a31af55d676" xlink:href="kg-20250930.xsd#kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock_06d31e02-8e7e-42d3-8d54-9a31af55d676" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuableTreasurySharesRetained_cc565c78-86d2-460d-b042-59bd865d54d2" xlink:href="kg-20250930.xsd#kg_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuableTreasurySharesRetained"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuableTreasurySharesRetained_cc565c78-86d2-460d-b042-59bd865d54d2" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionSharePrice_7edf43f9-fb18-414f-8384-a592056b2be5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionSharePrice"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock_31a2c846-bbe2-4c1c-b600-b7393f3de4da" xlink:href="kg-20250930.xsd#kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock_31a2c846-bbe2-4c1c-b600-b7393f3de4da" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_922cb2b1-c231-4159-9224-3a11009b53e7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_922cb2b1-c231-4159-9224-3a11009b53e7" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders_a9b8a620-4726-4c35-a511-2a50bcf42075" xlink:href="kg-20250930.xsd#kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders_a9b8a620-4726-4c35-a511-2a50bcf42075" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService_26937e45-cac0-437b-bfce-965671bc1760" xlink:href="kg-20250930.xsd#kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService_26937e45-cac0-437b-bfce-965671bc1760" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement_0fb03350-a6a9-4a10-a384-989b76ceec1e" xlink:href="kg-20250930.xsd#kg_BusinessCombinationConsiderationTransferredIntercompanySettlement"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement_0fb03350-a6a9-4a10-a384-989b76ceec1e" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferred1_4ea8d123-3326-4555-8c4d-eea61c642892" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferred1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_9044a774-1fc0-4b50-b203-8b3ee0d3b5c9" xlink:to="loc_us-gaap_BusinessCombinationConsiderationTransferred1_4ea8d123-3326-4555-8c4d-eea61c642892" xlink:type="arc" order="10"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/BusinessCombinationScheduleofPurchasePriceofAssetsandLiabilitiesAssumedDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#BusinessCombinationScheduleofPurchasePriceofAssetsandLiabilitiesAssumedDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/BusinessCombinationScheduleofPurchasePriceofAssetsandLiabilitiesAssumedDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_cc582273-d5df-49d9-acd0-cf456ed143dd" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_cc582273-d5df-49d9-acd0-cf456ed143dd" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis_0149bd90-0d7d-4f3c-a1b7-74ad7fb81d2d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_cc582273-d5df-49d9-acd0-cf456ed143dd" xlink:to="loc_us-gaap_BusinessAcquisitionAxis_0149bd90-0d7d-4f3c-a1b7-74ad7fb81d2d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_0149bd90-0d7d-4f3c-a1b7-74ad7fb81d2d_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_0149bd90-0d7d-4f3c-a1b7-74ad7fb81d2d" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_0149bd90-0d7d-4f3c-a1b7-74ad7fb81d2d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_b374c57a-3a98-4962-afd6-8d7262bfc3f9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_0149bd90-0d7d-4f3c-a1b7-74ad7fb81d2d" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_b374c57a-3a98-4962-afd6-8d7262bfc3f9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_37d3b81c-74e3-45f1-9336-1b7c9238763e" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain_b374c57a-3a98-4962-afd6-8d7262bfc3f9" xlink:to="loc_kg_KestrelGroupLtd.Member_37d3b81c-74e3-45f1-9336-1b7c9238763e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale_15dac359-104c-4323-b825-a026bf358531" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale_15dac359-104c-4323-b825-a026bf358531" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities_77f5c5c7-a8ce-4358-ab29-9fcfeae34f8a" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities_77f5c5c7-a8ce-4358-ab29-9fcfeae34f8a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments_ac9f8641-d17f-4d28-8b67-8153c76815d6" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments_ac9f8641-d17f-4d28-8b67-8153c76815d6" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments_f6abc100-4bab-4ab6-9b4d-dd847f3a411a" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments_f6abc100-4bab-4ab6-9b4d-dd847f3a411a" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_09072379-11e7-4d43-b635-31046655f5b9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_09072379-11e7-4d43-b635-31046655f5b9" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents_383ea170-2022-4545-97cd-300ff2214d27" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents_383ea170-2022-4545-97cd-300ff2214d27" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome_7ddc53c1-8fac-4730-9ac5-2fb594e23f02" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome_7ddc53c1-8fac-4730-9ac5-2fb594e23f02" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet_795633d6-3991-4dd2-92b4-7fa30ad83b6e" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet_795633d6-3991-4dd2-92b4-7fa30ad83b6e" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses_60526de8-1a60-4c1e-b508-390354820e64" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses_60526de8-1a60-4c1e-b508-390354820e64" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty_25a73007-c3c0-43ac-8536-900021200446" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty_25a73007-c3c0-43ac-8536-900021200446" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_e75897ee-fd48-463f-8a1e-4660b9178c5d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_e75897ee-fd48-463f-8a1e-4660b9178c5d" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_f010aeaf-7f5c-4c85-a3a3-feaed72cf191" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_f010aeaf-7f5c-4c85-a3a3-feaed72cf191" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther_ec0eae19-5241-461e-be96-a2c5435a9163" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther_ec0eae19-5241-461e-be96-a2c5435a9163" xlink:type="arc" order="12"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale_15fe9426-1015-448b-bad7-116cbf20edc3" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale_15fe9426-1015-448b-bad7-116cbf20edc3" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses_6f93a010-8834-473d-8cc6-b3bb5a1bea85" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses_6f93a010-8834-473d-8cc6-b3bb5a1bea85" xlink:type="arc" order="14"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums_05d909b9-fd06-498d-9447-6720b979b99d" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums_05d909b9-fd06-498d-9447-6720b979b99d" xlink:type="arc" order="15"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities_a825714f-3c0b-4677-9033-79e73393cfe3" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities_a825714f-3c0b-4677-9033-79e73393cfe3" xlink:type="arc" order="16"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt_2a393506-c7a7-4c9e-8d27-0379868c5a1c" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt_2a393506-c7a7-4c9e-8d27-0379868c5a1c" xlink:type="arc" order="17"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale_825a0acf-3e50-438e-b31e-2e36879b95dd" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale_825a0acf-3e50-438e-b31e-2e36879b95dd" xlink:type="arc" order="18"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_9590eb8b-98a1-491d-8321-3db7177a4ae3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_9590eb8b-98a1-491d-8321-3db7177a4ae3" xlink:type="arc" order="19"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_ced432ff-4295-4b15-bc47-ac464d567682" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_ced432ff-4295-4b15-bc47-ac464d567682" xlink:type="arc" order="20"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferred1_ede2682c-8b1c-46c3-9364-411e513cd278" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferred1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems_cde94316-5369-4d71-bd93-816074d57f14" xlink:to="loc_us-gaap_BusinessCombinationConsiderationTransferred1_ede2682c-8b1c-46c3-9364-411e513cd278" xlink:type="arc" order="21"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.kestrelgroup.com/role/BusinessCombinationScheduleofIntangibleAssetsAcquiredDetails" xlink:type="simple" xlink:href="kg-20250930.xsd#BusinessCombinationScheduleofIntangibleAssetsAcquiredDetails"/>
  <link:definitionLink xlink:role="http://www.kestrelgroup.com/role/BusinessCombinationScheduleofIntangibleAssetsAcquiredDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_b7dac772-ca84-4ef1-8561-6d32e47a8fff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable_8054b6c8-a3b6-45eb-b892-e71ee1590dd4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_b7dac772-ca84-4ef1-8561-6d32e47a8fff" xlink:to="loc_us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable_8054b6c8-a3b6-45eb-b892-e71ee1590dd4" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis_ce375a9f-4a30-4262-9a12-c61a1fbbe8d2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable_8054b6c8-a3b6-45eb-b892-e71ee1590dd4" xlink:to="loc_us-gaap_BusinessAcquisitionAxis_ce375a9f-4a30-4262-9a12-c61a1fbbe8d2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_ce375a9f-4a30-4262-9a12-c61a1fbbe8d2_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_ce375a9f-4a30-4262-9a12-c61a1fbbe8d2" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_ce375a9f-4a30-4262-9a12-c61a1fbbe8d2_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_1b954d87-0d92-4885-80ce-57c038a2c3ae" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_ce375a9f-4a30-4262-9a12-c61a1fbbe8d2" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_1b954d87-0d92-4885-80ce-57c038a2c3ae" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member_0aabce08-c8ff-42f7-a384-6bc9986cb115" xlink:href="kg-20250930.xsd#kg_KestrelGroupLtd.Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain_1b954d87-0d92-4885-80ce-57c038a2c3ae" xlink:to="loc_kg_KestrelGroupLtd.Member_0aabce08-c8ff-42f7-a384-6bc9986cb115" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedAssetAcquiredIdentifiableIntangibleAssetValueOfBusinessAcquired_e9881389-3333-41cc-a5f5-43689eb4c5c3" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedAssetAcquiredIdentifiableIntangibleAssetValueOfBusinessAcquired"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_b7dac772-ca84-4ef1-8561-6d32e47a8fff" xlink:to="loc_kg_BusinessCombinationRecognizedAssetAcquiredIdentifiableIntangibleAssetValueOfBusinessAcquired_e9881389-3333-41cc-a5f5-43689eb4c5c3" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedAssetAcquiredIdentifiableIntangibleAssetFairValueDiscountOnAcquiredReserves_d90ef6ae-cf40-44dc-b31f-b3ceb0068eb5" xlink:href="kg-20250930.xsd#kg_BusinessCombinationRecognizedAssetAcquiredIdentifiableIntangibleAssetFairValueDiscountOnAcquiredReserves"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_b7dac772-ca84-4ef1-8561-6d32e47a8fff" xlink:to="loc_kg_BusinessCombinationRecognizedAssetAcquiredIdentifiableIntangibleAssetFairValueDiscountOnAcquiredReserves_d90ef6ae-cf40-44dc-b31f-b3ceb0068eb5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_0a7ff63d-0c41-4881-98ec-d30c0f9f9aa6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_b7dac772-ca84-4ef1-8561-6d32e47a8fff" xlink:to="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_0a7ff63d-0c41-4881-98ec-d30c0f9f9aa6" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists" xlink:type="simple" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-roles-2025.xsd#eedm"/>
  <link:definitionLink xlink:role="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_058ca443-2aa1-418b-a8ea-87ead6e750c3" xlink:href="kg-20250930.xsd#kg_OtherInvestmentsAndEquityMethodInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:to="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_058ca443-2aa1-418b-a8ea-87ead6e750c3" xlink:type="arc" order="31"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:type="arc" order="31"/>
  </link:definitionLink>
</link:linkbase>
