1 From: Ohio Farmers Insurance Company 1 Park Circle, Westfield Center Ohio 44251 United States of America To: Argo International Holdings Limited 6 Devonshire Square London, EC2M 4YE United Kingdom 2 February 2023 Dear Sirs or Madams, Letter Deed of Amendment 1. We refer to the share purchase agreement for the sale and purchase of the entire issued share capital of Argo Underwriting Agency Limited between Argo International Holdings Limited (the “Seller”) and Ohio Farmers Insurance Company (the “Purchaser”), dated 8 September 2022 (the “Agreement”). 2. This Letter (the “Letter”) shall be a Share Purchase Document for the purposes of the Agreement. Unless the context requires otherwise, terms used in this Letter but not otherwise defined herein shall have the meanings given to them in the Agreement. Unless the context requires otherwise, references in this Letter to “Clauses” are to Clauses of the Agreement. 3. The Agreement shall be hereby amended in the manner set out in paragraphs 3.1 to 3.11 below, namely: 3.1 Clause 1.1 is hereby amended so that the following definitions are included in the appropriate place, so as to ensure that all definitions remain in alphabetical order following such amendment: (a) “COVID Recoveries” has the meaning given in paragraph 1.1 of Part A of Schedule 19 (COVID Recoveries); (b) “Escrow Account” has the meaning given in paragraph 1.1 of Part A of Schedule 19 (COVID Recoveries); (c) “Escrow Agent” has the meaning given in paragraph 1.1 of Part A of Schedule 19 (COVID Recoveries); (d) “Escrow Agreement” has the meaning given in paragraph 1.1 of Part A of Schedule 19 (COVID Recoveries); (e) “Escrow Amount” has the meaning given in paragraph 1.1 of Part A of Schedule 19 (COVID Recoveries); Exhibit 10.34

2 (f) “Outstanding COVID 19 Recoveries Amount” has the meaning given in paragraph 1.1 of Part A of Schedule 19 (COVID Recoveries); and (g) “Reinsurance Protocol” means Schedule 14 (Reinsurance Protocols). 3.2 The definition of “Claim” in Clause 1.1 is hereby amended as follows: ““Claim” means any proceedings, claim, suit or action made by a Party arising out of the Share Purchase Documents (excluding the TPV/ PRI Reinsurance Agreement, the TPV/ PRI Claims Management Agreement, the D&F/ Casualty Reinsurance Agreement, the D&F/ Casualty Claims Management Agreement, Fronting Agreement, the Transitional Services Agreement, the Reinsurance Protocol and any other documents in the Agreed Form) or the transactions contemplated hereby;” 3.3 Clause 5.1 is hereby amended by: (a) deleting the full stop at the end of Clause 5.1(b) and replacing it with a semi- colon; and (b) inserting the words “as adjusted in accordance with paragraph 2.5 of Part A of Schedule 19 (COVID Recoveries)” at the end of Clause 5.1, immediately below Clause 5.1(b). 3.4 Clause 5.2 is deleted in its entirety and replaced with the following: “5.2 At Completion, the Purchaser shall pay: (a) to the Seller in cash an amount which is equal to the sum of: (i) the Base Consideration; (ii) plus the amount (if any) by which the Estimated Completion Net Assets exceed the Base Net Assets; (iii) minus the amount (if any) by which the Estimated Completion Net Assets fall short of the Base Net Assets; (iv) minus the Escrow Amount, (the “Completion Payment”); and (b) to the Escrow Agent (by way of payment to the Escrow Account) an amount in cash equal to the Escrow Amount, which amount shall be held by the Escrow Agent in accordance with the Escrow Agreement and subject to Schedule 19 (COVID Recoveries).” 3.5 a new Clause 8.4 is included, as follows: “8.4 The provisions of Schedule 19 shall apply in respect of the COVID Recoveries.” 3.6 Clause 12.17 (b) is amended as follows:

3 negotiate and agree with all third party capital providers (including excess of loss, quota share reinsurers and banks) that have provided FAL on behalf of the Argo Active Corporate Members (other than for 2020 and prior YOAs), including pursuant to any replacement excess of loss reinsurance contracts as described in Clause 12.6 above, such revised FAL providers’ deed(s), and Lloyd’s comfort letters and such other documents as may reasonably be required to release the Retained Group from ongoing responsibility to such third party capital providers with effect from Completion, or in any event, as soon as practicable thereafter (including by arranging for the termination of the FAL providers deed (2022 and prior underwriting years) dated 13 January 2022 between Argo (No. 604) Limited, Argo Group International Holdings Ltd., Argo Managing Agency Limited, Arch Reinsurance Ltd., Everest Reinsurance (Bermuda) Ltd. And XL Bermuda Ltd with effect from Completion, or in any event, as soon as practicable thereafter); 3.7 paragraph 1.8(a) of Part A of Schedule 3 is amended as follows: (a) duly executed counterparts of the Share Purchase Documents (excluding the Confidentiality Agreement) not referred to in 1.2 or 1.3 above and , the Transitional Services Agreement and the Escrow Agreement; 3.8 paragraph 1(b) of Part B of Schedule 3 is amended as follows: (b) procure the delivery to the Seller of duly executed counterparts of the Escrow Agreement and the Share Purchase Documents (excluding the Confidentiality Agreement) to which the Purchaser or any member of the Purchaser’s Group is a party to; 3.9 paragraph 3.1(a)(iv) of Schedule 11 is amended as follows: “the Completion Balance Sheet shall be prepared on the basis set out in paragraphs 3.2 to 3.4 below.” 3.10 a new paragraph 3.4 of Schedule 11 shall be inserted, as follows: 3.4 The Completion Balance Sheet will include the Outstanding COVID 19 Recoveries Amount which amount shall, for the avoidance of doubt, be recognised (without double counting) as an “Asset”. 3.11 a new Schedule 19 is inserted, in the form set out in the Appendix to this Letter. 4. Except as expressly amended or waived in this Letter, the Agreement shall remain in full force and effect and the Parties shall continue to be bound by their obligations contained therein. 5. Except as expressly provided for in this Letter, a person who is not a party to this Letter shall not have any rights under the Contracts (Rights of Third Parties) Act 1999 to enforce any of the provisions of this Letter. 6. This Letter constitutes the entire agreement between the Parties in respect of its subject matter. Each Party acknowledges that in entering into this Letter it does not rely on any statement, representation, assurance or warranty that is not set out in this Letter. Each

4 Party agrees that it shall have no claim for innocent or negligent misrepresentation based on any statement in this Letter. Nothing in this paragraph shall limit or exclude any liability for fraud. 7. Clauses 22 to 24, 26 to 31 and 33 to 37 of the Agreement shall apply to this Letter as if they were set out in full in this Letter, and any references therein to “this Agreement” are read to mean “this Letter”. 8. Please confirm your acknowledgement to and acceptance of the terms and conditions of this Letter by countersigning and dating the duplicate of this Letter, and returning to the Purchaser. [Signature pages to follow]

5 IN WITNESS whereof this Letter has been executed and delivered as a Deed on the date first above written. Executed as a deed by OHIO FARMERS INSURANCE COMPANY, a corporation incorporated under the laws of the State of Ohio, acting by person(s) who, in accordance with the laws of that territory, are acting under the authority of the company __________________________ Name: Position: In the presence of: Witness signature: _____________________ Name of witness: _____________________ Address: _____________________ _____________________ _____________________ Occupation: _____________________ ) ) ) ) ) )

6 IN WITNESS whereof this Letter has been executed and delivered as a Deed on the date first above written. Executed as a deed by ARGO INTERNATIONAL HOLDINGS LIMITED __________________________ Name: Position: In the presence of: Witness signature: _____________________ Name of witness: _____________________ Address: _____________________ _____________________ _____________________ Occupation: _____________________ ) ) )