SHARE PURCHASE AGREEMENT

Exhibit 10.7

SHARE PURCHASE AGREEMENT

THIS SHARE PURCHASE AGREEMENT (this “Agreement”) is made and entered into as of this 28th day of May 2013, between Codan Trust Company Limited solely in its capacity as trustee of a trust dated 3 April 2013 and known as the Prometheus Trust (the “Trust” and in such capacity the “Investor”) and Endurance Specialty Holdings Ltd., an exempted company incorporated in Bermuda as a holding company (the “Company”).

WITNESSETH:

WHEREAS, the Company desires to sell to the Investor and the Investor desires to acquire from the Company 50,635 ordinary shares (the “Purchase Shares”), par value $1.00 per share, of the Company (the “Ordinary Shares”), upon the terms and conditions set forth in this Agreement.

NOW, THEREFORE, in consideration of the mutual terms and other agreements set forth herein, the parties hereto hereby agree as follows:

ARTICLE I.

SALE AND PURCHASE

SECTION 1.1. Agreement to Sell and to Purchase

On the date hereof and upon the terms set forth in this Agreement, the Investor agrees to purchase and accept and the Company agrees to sell and issue to the Investor the Purchase Shares.

SECTION 1.2. Closing

The closing of such sale and purchase (the “Closing”) shall take place remotely via the exchange of documents and signatures at 7:00 am. New York City time, on the date hereof. At or promptly following the Closing, the Company shall deliver to the Investor or its designees a certified copy of an extract of the register of shareholders of the Company evidencing the registration of the Purchase Shares as held by the Investor and duly executed stock certificates or other instruments evidencing the Purchase Shares. In consideration and exchange for the Purchase Shares, the Investor shall thereupon pay to the Company the Purchase Price as provided in Section 1.3 hereof.

SECTION 1.3. Purchase Price

At the Closing, the Investor shall deliver to the Company cash in the aggregate amount of US$2,500,000 (the “Purchase Price”), payable by wire transfer in immediately available funds to the account or accounts specified by the Company.

ARTICLE II.

REPRESENTATIONS AND WARRANTIES OF THE COMPANY

The Company hereby represents and warrants to the Investor, as of the date hereof, as follows:

SECTION 2.1. Organization, Good Standing, Corporate Power and Qualification

The Company is an exempted company incorporated in Bermuda as a holding company, is duly organized and validly existing under the laws of Bermuda and has all requisite organizational power and authority to carry on its business as presently conducted and as proposed to be conducted. The Company is duly qualified to transact business and is in good standing in each jurisdiction in which the failure to so qualify or to be in good standing would have a material adverse effect on the Company’s business, assets, properties or results of operations.

SECTION 2.2. Issuance of the Purchase Shares

The Purchase Shares, when issued, sold and delivered in accordance with the terms and for the consideration set forth in this Agreement, will be validly issued, fully paid and nonassessable and free of restrictions on transfer other than restrictions on transfer under applicable state, federal or foreign securities laws and liens or encumbrances created by or imposed by the Investor. Assuming the accuracy of the representations of the Investor in Article III of this Agreement, the Purchase Shares will be issued in compliance with all applicable state, federal and foreign securities laws.

SECTION 2.3. Authorization; Validity of Agreement

All organizational action required to be taken by the Company’s board of directors and shareholders in order to authorize the Company to enter into this Agreement, and to issue all of the Purchase Shares contemplated to be issued hereunder at the Closing, has been taken prior to the Closing. All action on the part of the officers of the Company necessary for the execution and delivery of this Agreement and the issuance and delivery of the Purchase Shares has been taken prior to the Closing. This Agreement, when executed and delivered by the Company, shall constitute a valid and legally binding obligation of the Company, enforceable against the Company in accordance with its terms except (i) as limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance, or other laws of general application relating to or affecting the enforcement of creditors’ rights generally or (ii) as limited by laws relating to the availability of specific performance, injunctive relief, or other equitable remedies.

SECTION 2.4. No Conflict or Violation

The execution, delivery and performance by the Company of this Agreement does not violate or conflict with any provision of its memorandum of association or bye-laws and does not violate any provision of law, or any order, judgment or decree of any court or other governmental or regulatory authority, nor violate or result in a breach of or constitute (with due notice or lapse of time or both) a default under any material contract, lease, loan agreement, mortgage, security agreement or other material agreement or instrument to which the Company is a party or by which it is bound.

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SECTION 2.5. Consents and Approvals

Assuming the accuracy of the representations made by the Investor in Article III of this Agreement, no consent, approval, order or authorization of, or registration, qualification, designation, declaration or filing with, any federal, state, local or foreign governmental authority is required on the part of the Company in connection with the consummation of the transactions contemplated by this Agreement, except, if applicable, for the filing of a Supplemental Listing Application with the New York Stock Exchange and filings pursuant to Regulation D of the U.S. Securities Act of 1933, as amended (the “Securities Act”), and applicable state securities laws, which have been made or will be made in a timely manner.

SECTION 2.6. No Broker

Neither the Company nor any of its representatives has any contract, arrangement or understanding with any broker, finder or similar agent with respect to the transactions contemplated by this Agreement, and no commission or other remuneration has been or will be paid or given, directly or indirectly, for soliciting or finding investors.

SECTION 2.7. No Material Misstatements or Omissions

None of the documents filed with the U.S. Securities and Exchange Commission (the “Commission”) by the Company in the 12 months prior to the date hereof contained an untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary to make the statements therein, in light of the circumstances under which they were made, not misleading, as of the date of this Agreement, other than the information regarding the transactions contemplated by this Agreement and the other transactions related to the hiring of John R. Charman by the Company which shall be reported on a Current Report on Form 8-K following the consummation of such transactions. The Company is not required to and does not propose to, as at the date of this Agreement, make any filings with the Commission in relation to any material business or financial disclosure of the Company which has not been the subject of a prior filing with the Commission, other than the information regarding the transactions contemplated by this Agreement and the other transactions related to the hiring of John R. Charman by the Company, which shall be reported on a Current Report on Form 8-K following the consummation of such transactions.

SECTION 2.8. Offer/Sale Outside of the United States

Neither the Company nor any of its representatives has made any directed selling efforts in the United States and no offers were made in the United States. This is an “offshore transaction” as defined in Regulation S of the Securities Act.

SECTION 2.9. No Other Representations and Warranties

Except for the representations and warranties expressly made by the Company in this Article II, the Company does not make any representation or warranty with respect to the Company or its respective businesses, operations, assets, liabilities, condition (financial or otherwise) or prospects.

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ARTICLE III.

REPRESENTATIONS AND WARRANTIES OF THE INVESTOR

The Investor hereby represents and warrants to the Company, as of the date hereof, as follows:

SECTION 3.1. Authority; Validity of Agreement

All organizational action required to be taken by the Investor’s trustees in order to authorize the Company to enter into this Agreement, and to carry out its obligations hereunder, has been taken prior to the Closing. All action on the part of the trustees of the Investor necessary for the execution and delivery of this Agreement and the carrying out of the Investor’s obligations hereunder has been taken prior to the Closing. This Agreement, when executed and delivered by the Investor, shall constitute a valid and legally binding obligation of the Investor, enforceable against the Investor in accordance with its terms except (i) as limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance, or other laws of general application relating to or affecting the enforcement of creditors’ rights generally or (ii) as limited by laws relating to the availability of specific performance, injunctive relief, or other equitable remedies.

SECTION 3.2. No Conflict or Violation

The execution, delivery and performance by the Investor of this Agreement does not violate any provision of law, or any order, judgment or decree of any court or other governmental or regulatory authority, nor violate or result in a breach of or constitute (with due notice or lapse of time or both) a default under any material contract, lease, loan agreement, mortgage, security agreement or other material agreement or instrument to which the Investor is a party or by which it is bound.

SECTION 3.3. Consents and Approvals

No consent, approval or authorization of, or filing, registration or qualification with, any governmental authority on the part of the Investor is required as a condition to the execution, delivery and performance of this Agreement or the purchase of the Purchase Shares contemplated hereby.

SECTION 3.4. Exemption from Securities Act

The Investor has been advised and understands that (i) the Purchase Shares have not been registered under the Securities Act, or any state securities laws and are being sold pursuant to Regulation S, therefore, cannot be resold until the applicable distribution compliance period is satisfied or they are registered under the Securities Act and applicable state securities laws, or unless an exemption from such registration requirements is available, (ii) the Investor may be required to hold, and continue to bear the economic risk of its investment in, the Purchase Shares indefinitely, unless the offer and sale of such Purchase Shares is subsequently

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registered under the Securities Act and all applicable state securities laws or an exemption from such registration is available, (iii) Rule 144 promulgated under the Securities Act is not presently available with respect to the sale of the Purchase Shares, (iv) when and if the Purchase Shares may be disposed of without registration under the Securities Act in reliance on Rule 144 of the Securities Act, the amount of Purchase Shares that may be disposed of may be limited in accordance with the terms and conditions of such Rule and (v) if an exemption under Rule 144 of the Securities Act is not available, the public offer or sale of the Purchase Shares without registration will require compliance with some other exemption under the Securities Act.

SECTION 3.5. Accredited Investor; Non-U.S. Person

The Investor is an “accredited investor” as such term is defined in Rule 501(a) of the Securities Act and has such knowledge and experience in financial and business matters that it is capable of evaluating the merits and risks of the investment contemplated by this Agreement. The Investor represents it is a not a U.S. Person as such term is defined under Rule 902 of the Securities Act. The Investor further represents that its assets are in excess of U.S. $5,000,000. The Investor is able to bear the economic risk of its investment in the Company (including a complete loss of such investment).

SECTION 3.6. Investment Purpose

The Investor is acquiring the Purchase Shares solely for its own account for investment and not with a view toward the distribution thereof within the meaning of Section 11 of the Securities Act. Furthermore, the Investor is not acquiring the Purchase Shares for the account or benefit of any U.S. Person. The Investor is aware that, except as may be provided in any other agreement between the Investor and the Company, the Company is under no obligation to effect any registration with respect to the Purchase Shares or to file for or comply with any exemption from registration. The Investor’s decision to purchase the Purchase Shares was made outside of the United States (as defined in Regulation S). Furthermore, the Investor agrees to comply with the distribution compliance period under Regulation S and will not resell the Purchase Shares until the 40 day distribution compliance period has elapsed.

SECTION 3.7. Economic Risk

The Investor understands that it must bear the economic risk of this investment indefinitely unless the Purchase Shares are registered pursuant to the Securities Act or an exemption from such registration is available, and unless the disposition of the Purchase Shares is qualified under applicable state securities laws or an exemption from such qualification is available. The Investor further understands that there is no assurance that any exemption from the Securities Act will be available, or, if available, that such exemption will allow the Investor to transfer any or all of the Purchase Shares, in the amounts, or at the time the Investor might propose. The Investor has independently and without reliance upon the Company, any Affiliate thereof or any agent of the foregoing, and based on such documents and information as the Investor has deemed appropriate, made its own appraisal of and investigation into the business, operations, property, financial and other condition of the Company and made its own investment decision with respect to the investment represented by the Purchase Shares. The Investor has consulted, to the extent deemed appropriate by the Investor, with the Investor’s own advisers as

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to the financial, tax, legal and related matters concerning an investment in the Purchase Shares and on that basis understands the financial, legal, tax and related consequences of an investment in the Purchase Shares, and believes that an investment in the Purchase Shares is suitable and appropriate for the Investor.

SECTION 3.8. Excluded Information

The Investor has sufficient knowledge and experience in financial and business matters so as to be capable of evaluating the merits and risks of the transactions contemplated by this Agreement. The Investor acknowledges that the Company is privy to material, non-public information not known to the Investor (the “Excluded Information”). Subject to Section 2.7, the Investor hereby agrees that the Company shall not be obligated to disclose any Excluded Information or have any liability to the Investor with respect to any such non-disclosure. The Investor understands and agrees that the Company makes no representation or warranty whatsoever with respect to the business, condition (financial or otherwise), properties, prospects, creditworthiness, status or affairs of the Company or with respect to the value of the Purchase Shares. Subject to the terms of Article II, the Investor hereby waives any and all claims and causes of action now or hereafter arising against the Company based upon or relating to the value of the Company or the Purchase Shares and further covenants not to sue the Company or any of its directors, officers, employees, agents or affiliates for any loss, damage or liability arising from or relating to the value of the Company or the Purchase Shares in relation to this Agreement.

SECTION 3.9. No Broker

There are no claims for brokerage commissions or finder’s fees or similar compensation in connection with the transactions contemplated by this Agreement based on any arrangement made by or on behalf of the Investor.

SECTION 3.10. No other Representations and Warranties

Except for the representations and warranties expressly made by the Investor in this Article III, the Investor does not make any representation or warranty with respect to its investment in the Purchase Shares.

ARTICLE IV.

MISCELLANEOUS PROVISIONS

SECTION 4.1. Limited Recourse

Notwithstanding anything else herein contained, the Investor, has entered this Agreement solely in its capacity as trustee of the Trust and the benefits of this Agreement are held by the Investor subject to the provisions of the Trust. Notwithstanding any other provision of this Agreement, any and all liabilities of the Investor created by this Agreement shall be limited to the extent such liability can be met from and out of the property from time to time subject to the trusts of the Trust and, accordingly:

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SECTION 4.2. Successors and Assigns; No Third Party Beneficiaries

This Agreement shall inure to the benefit of, and be binding upon, the parties hereto and their respective successors. No party hereto shall assign or delegate any of the rights or obligations created under this Agreement without the prior written consent of the other party hereto. Nothing in this Agreement shall confer upon any person or entity not a party to this Agreement, or the legal representatives of such person or entity, any rights or remedies of any nature or kind whatsoever under or by reason of this Agreement.

SECTION 4.3. Fees and Expenses

All legal, accounting and other fees, costs and expenses incurred in connection with this Agreement and the transactions contemplated hereby shall be paid by the party incurring such fees, costs or expenses.

SECTION 4.4. Notices

Unless otherwise specified herein, all notices, consents, approvals, reports, designations, requests, waivers, elections and other communications authorized or required to be given pursuant to this Agreement shall be in writing and shall be deemed to have been given (a) when personally delivered, (b) when transmitted via facsimile to the number set out below, if the sender on the same day sends a confirming copy of such notice by a recognized overnight delivery service (charges prepaid), (c) the day following the day (except if not a Business Day then the next Business Day) on which the same has been delivered prepaid to a reputable national overnight courier service, (d) when transmitted via email (including via attached pdf document) to the email address set out below, if the sender on the same day sends a confirming copy of such notice by a recognized overnight delivery service (charges prepaid) or (e) the third Business Day following the day on which the same is sent by certified or registered mail, postage prepaid, in each case to the respective parties as applicable, at the address, facsimile number or email address set forth below (or such other address, facsimile number or email address as the Investor may specify by notice to the Company in accordance with this Section 4.4):

If to the Investor, to:

Codan Trust Company Limited

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as Trustee of the Prometheus Trust

Richmond House

12 Par-la-Ville Road

Hamilton HM 08

Bermuda

Fax: 441 ###-###-####

Email: ***@***

with a copy (which shall not constitute notice) to:

Alec Anderson

Conyers Dill and Pearman Limited

12 Par-la-Ville Road

Hamilton HM 08

Bermuda

Fax: 441 ###-###-####

Email: ***@***

If to the Company, to:

Endurance Specialty Holdings Ltd.

Wellesley House

90 Pitts Bay Road

Pembroke HM 08, Bermuda

Fax: 441 ###-###-####

Attention: John Del V Col

Email: ***@***

with a copy (which shall not constitute notice) to:

Willkie Farr & Gallagher LLP

787 Seventh Avenue

New York, NY 10019

Fax: (212)  ###-###-####

Attention: Michael Groll, Esq.

Email: ***@***

SECTION 4.5. Entire Agreement

This Agreement and the agreements contemplated hereby represent the entire agreement and understanding of the parties with reference to the transactions set forth herein and no representations or warranties have been made in connection with this Agreement other than those expressly set forth herein. This Agreement and the agreements contemplated hereby supersede all prior negotiations, discussions, correspondence, communications, understandings and agreements between the parties relating to the subject matter of this Agreement and all prior drafts of this Agreement, all of which are merged into this Agreement. No prior drafts of this Agreement and no words or phrases from any such prior drafts shall be admissible into evidence in any action or suit involving this Agreement.

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SECTION 4.6. Severability

This Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Agreement or of any other term or provision hereof. Any provision of this Agreement held invalid or unenforceable only in part will remain in full force and effect to the extent not held invalid or unenforceable.

SECTION 4.7. Titles and Headings

The Article and Section headings and any table of contents contained in this Agreement are solely for convenience of reference and shall not affect the meaning or interpretation of this Agreement or of any term or provision hereof.

SECTION 4.8. Signatures and Counterparts

This Agreement may be executed and delivered (including by facsimile transmission) in two (2) or more counterparts, each of which shall be deemed to be an original and all which taken together shall constitute one and the same agreement.

SECTION 4.9. Legal Counsel and Interpretation

Each of the parties hereto acknowledges that each party to this Agreement has been represented by counsel in connection with this Agreement and the transactions contemplated by this Agreement. Accordingly, any rule of law, or any legal decision that would require interpretation of any claimed ambiguities in this Agreement against the party that drafted it has no application and is expressly waived.

SECTION 4.10. Survival

All covenants, agreements, representations and warranties made herein shall survive the execution and delivery hereof.

SECTION 4.11. Dispute Resolution

All disputes, controversies or claims arising out of, relating to or in connection with this Agreement, or the breach, termination or validity thereof, shall be finally settled by arbitration. The arbitration shall be conducted in accordance with the arbitration procedures set forth in Section 7.7 of the Employment Agreement, dated the date hereof, between the Company and John R. Charman.

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SECTION 4.12. Governing Law

THIS AGREEMENT SHALL BE GOVERNED AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF BERMUDA, WITHOUT REGARD TO THE CONFLICTS OF LAW PRINCIPLES THEREOF. SUBJECT TO SECTION 4.11, THE PARTIES SUBMIT TO THE NON-EXCLUSIVE JURISDICTION OF THE COURTS OF BERMUDA IN RELATION TO THIS AGREEMENT.

[Remainder of Page Intentionally Blank]

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date first above written.

[Signature page for The Prometheus Trust SPA]

[Signature page for The Prometheus Trust SPA]