ENDURANCE SPECIALTY HOLDINGS LTD. SHAREHOLDER AGREEMENT

Exhibit 10.8

ENDURANCE SPECIALTY HOLDINGS LTD.

SHAREHOLDER AGREEMENT

This Shareholder Agreement (this “Agreement”) is dated as of this 28th day of May, 2013 and entered into by and among John R. Charman (the “Executive”), Dragon Global Holdings Ltd. (the “Investor”), and Endurance Specialty Holdings Ltd., an exempted company incorporated in Bermuda as a holding company (the “Company”).

RECITALS

WHEREAS, the Company desires to sell to the Investor and the Investor desires to acquire from the Company 506,350 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 that certain Share Purchase Agreement, between the Company and the Investor, dated as of the date hereof (the “Share Purchase Agreement”);

WHEREAS, in connection with the hiring of the Executive as the Chairman and Chief Executive Officer of the Company, the Company has granted to the Executive 708,890 Ordinary Shares (the “Restricted Shares”), upon the terms and conditions set forth in that certain Restricted Share Agreement, between the Company and the Executive, dated as of the date hereof (the “Restricted Share Agreement”);

WHEREAS, in connection with the hiring of the Executive as the Chairman and Chief Executive Officer of the Company, the Company has granted to the Executive an option to acquire 800,000 Ordinary Shares (the “Option Shares”), upon the terms and conditions set forth in that certain Option Agreement, between the Company and the Executive, dated as of the date hereof (the “Option Agreement”); and

WHEREAS, in connection with the Investor’s acquisition of the Purchase Shares, and the Executive’s acquisition of the Option Shares and Restricted Shares, the Company, the Executive and the Investor desire to enter into this Agreement.

NOW, THEREFORE, in consideration of the mutual covenants and agreements herein contained, the parties hereto hereby agree as follows:

(a) Prior to the earliest of (i) the five year anniversary of the date hereof, (ii) the death or Disability of the Executive, (iii) the date of termination of the Executive’s employment with the Company by the Company without Cause or by the Executive for Good Reason or (iv) the six month anniversary of the date of termination of the Executive’s employment with the Company by the Company with Cause or by the Executive without Good Reason (the “Transfer Restriction Termination Date”), neither the Executive nor the Investor will, directly or indirectly, Transfer any Purchase Shares, Restricted Shares or Option Shares (“Securities”) owned by the Executive or the Investor, except for Transfers to Permitted Transferees; provided, that following the two year anniversary of the date hereof, the Investor shall be permitted to sell without restriction up to 5% of the Purchase Shares in each 12 month

period following such two-year anniversary; and provided further that the Investor and the Executive may sell without restriction Securities in order to (i) fund the payment of the exercise price payable upon exercise of Options under the Option Agreement or (ii) reduce the aggregate value of the Securities held by the Investor and the Executive below the then applicable threshold for determining whether companies are required to notify U.S. federal antitrust authorities under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended.

(b) A Permitted Transferee of Securities pursuant to this Agreement may subsequently Transfer his, her or its Securities only to the Executive, the Investor or to a Person that is a Permitted Transferee of the Executive or the Investor. Each Permitted Transferee of the Executive or the Investor shall, and the Executive or the Investor shall use best efforts to cause such Permitted Transferee to, Transfer back to the Executive or the Investor (or to another Permitted Transferee of the Executive or the Investor) the Securities it acquired from the Executive or the Investor if such Permitted Transferee ceases to be a Permitted Transferee of the Executive or the Investor.

(c) Any Transfer of Securities in violation of this Section 1 shall, to the fullest extent permitted by law, be null and void ab initio, and the Company shall not, and shall instruct its transfer agent and other third parties not to, record or recognize any such purported transaction on the share register of the Company.

(d) So long as the Executive and the Investor are in compliance with Section 1(a), nothing set forth in Section 1 shall prohibit the Executive or the Investor from Transferring Securities pursuant to the terms of a Buyout Transaction.

(a) Prior to the Transfer Restriction Termination Date, the Executive and the Investor agree that the Executive and the Investor shall be present, in person or by proxy, at all meetings of the shareholders of the Company so that all of the Securities may be counted for the purpose of determining the presence of a quorum at such meetings.

(b) During the period from the last day of the Executive’s employment with the Company and to the date 6 months after that date (the “Standstill Period”), the Executive and the Investor agree that:

(i) Neither the Executive nor the Investor shall in any manner acquire, agree to acquire or make any proposal to acquire any securities or property of the Company or any of its subsidiaries or affiliates;

(ii) Neither the Executive nor the Investor shall make, or in any way participate in, directly or indirectly, any “solicitation” of “proxies”, or become a “participant” in any “solicitation” (as such terms are used in Regulation 14A under the Exchange Act) to vote or to seek to advise or influence any person to vote against any proposal or director nominee recommended to the shareholders of the Company or any of its subsidiaries or affiliates by at least a majority of the Board;

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(iii) Neither the Executive nor the Investor shall form, join or in any way participate in any group of Persons acquiring, holding, voting or disposing of any securities of the Company which would be required under Section 13(d) of the Exchange Act and the rules and regulations thereunder to file a statement on Schedule 13D with the SEC as a “person” within the meaning of Section 13(d)(3) of the Exchange Act; and

(iv) Neither the Executive nor the Investor shall otherwise act, alone or in concert with others, to seek to control or influence the management, Board or policies of the Company.

(a) All certificates representing any of the Purchased Shares, shall have endorsed thereon the following legend:

“The transferability of this certificate and the ordinary shares represented hereby are subject to the restrictions, terms and conditions (including restrictions against transfer) contained in a Shareholder Agreement entered into between the registered owner of such ordinary shares and the Company.

All certificates representing any of the Option Shares and Restricted Shares shall have endorsed thereon the respective legends set forth in the Option Agreement and the Restricted Share Agreement.

Prior to the second anniversary of this Agreement, the Company shall use commercially reasonable efforts to file and maintain an effective Registration Statement on Form S-3 with respect to those Securities which are not otherwise registered under the U.S. Securities Act of 1933, as amended, to provide the Investor and any of its Permitted Transferees, if applicable, the ability to resell such Securities, subject to any limitation under Section 1(a).

(a) Terms Defined. As used in this Agreement, the following terms have the respective meanings set forth below:

Board: shall mean the board of directors of the Company.

Business Day: shall mean any day other than a Saturday, Sunday or a day on which banks in New York, New York are authorized or obligated by law or executive order to close.

Buyout Transaction: shall mean a tender offer, exchange offer, merger, consolidation, amalgamation, scheme or arrangement, acquisition, business combination or similar transaction that has been approved by the Board (or that has become unconditional otherwise than as a result of an acceptance by the Investor), that offers each holder of Ordinary Shares (other than, if applicable, the Person proposing such transaction or other Persons

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participating in such transaction, including Persons who rollover their Ordinary Shares or other Securities) the opportunity to receive with respect to such holder’s Ordinary Shares the same consideration per Ordinary Share (which shall include, without limitation, cash and share election transactions) or otherwise contemplates the acquisition of Ordinary Shares beneficially owned by each such holder for the same consideration (which shall include, without limitation, cash and share election transactions); provided that the decision by certain holders to rollover their Ordinary Shares shall not exclude such a transaction from being considered a Buyout Transaction.

Change of Control: shall have the meaning set forth in the Employment Agreement.

Cause: shall have the meaning set forth in the Employment Agreement.

Disability: shall have the meaning set forth in the Employment Agreement.

Employment Agreement: shall mean the Employment Agreement, dated the date hereof, between the Company and the Executive, as such Employment Agreement may be amended from time to time.

Exchange Act: shall mean the U.S. Securities Exchange Act of 1934, as amended.

Good Reason: shall have the meaning set forth in the Employment Agreement.

Permitted Transferee: shall mean, (i) the Executive’s spouse or direct lineal descendants (including by adoption), (ii) any trust established for the sole benefit of the Executive or the Executive’s spouse or direct lineal descendants (including by adoption), (iii) any Person in which the direct or indirect and beneficial owner of all voting securities of such Person is the Executive or the Executive’s spouse or direct lineal descendants (including by adoption), (iv) the Executive’s heirs, executors, administrators or personal representatives upon the death, incompetency or disability of the Executive, and (v) any affiliate of such Executive that has been approved by the Board as a “Permitted Transferee” in writing prior to any transfer of Securities, which approval shall be granted by the Board unless the Board determines, in its sole and absolute discretion, that the applicable Transfer would result in an increased risk of adverse tax, regulatory or legal consequences to the Company, any of its subsidiaries or any of its shareholders; provided that, such trust or other Person shall only be a Permitted Transferee if such Person agrees in writing to be bound by the terms of Section 1.

Person: shall mean an individual, partnership (whether general or limited), joint-stock company, corporation, limited liability company, trust or unincorporated organization, and a government or agency or political subdivision thereof.

SEC: shall mean the Securities and Exchange Commission or any successor agency.

Transfer: shall mean (i) any sale, assignment, pledge, transfer, hypothecation or other disposition or encumbrance of Ordinary Shares, (ii) any purchase, sale and trading of puts, calls, options, variable forward contracts, equity swaps, collars, or other derivative securities

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based on the Ordinary Shares,(iii) any utilization of Ordinary Shares as collateral in a margin account or pledge of Ordinary Shares as security or collateral for any outstanding or new debt or (iv) any short sale of Ordinary Shares (except in connection with the exercise of the option under the Option Agreement), and each of “Transferred”, “Transferee” and “Transferor” have a correlative meaning.

(b) Directly or Indirectly. Where any provision in this Agreement refers to action to be taken by any Person, or which such Person is prohibited from taking, such provision shall be applicable whether such action is taken directly or indirectly by such Person.

(c) Governing Law. This Agreement shall be governed by and construed in accordance with the laws of Bermuda applicable to contracts made and to be performed entirely within Bermuda. Subject to Section 5(k), the parties submit to the non-exclusive jurisdiction of the Bermuda courts in relation to this Agreement.

(d) Section Headings. The headings of the sections and subsections of this Agreement are inserted for convenience only and shall not be deemed to constitute a part thereof.

(a) Notices.

(i) All communications under this Agreement shall be in writing and shall be delivered by hand or facsimile or mailed by overnight courier or by registered or certified mail, postage prepaid:

(A) if to the Executive, at the address of the Executive shown on signature page hereto or at such other address as the Executive may have furnished the Company in writing;

(B) if to the Investor, at the address or facsimile number of the Investor shown on signature page hereto or at such other address as the Investor may have furnished the Company in writing; and

(C) if to the Company, at Wellesley House, 90 Pitts Bay Road, Pembroke HM 08, Bermuda, marked for attention of John Del V Col, facsimile ###-###-####, with a copy (which shall not constitute notice) to Willkie Farr & Gallagher LLP, 787 Seventh Avenue, New York, NY 10019, facsimile ###-###-####, marked for attention of Michael Groll, Esq., or at such other address as it may have furnished in writing to the Investor.

(ii) Any notice so addressed shall be deemed to be given: if delivered by hand or facsimile, on the date of such delivery if a Business Day and delivered during regular business hours, otherwise the first Business Day thereafter; if mailed by overnight courier, on the first Business Day following the date of such mailing; and if mailed by registered or certified mail, on the third Business Day after the date of such mailing.

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(b) Successors and Assigns. This Agreement shall inure to the benefit of and be binding upon the successors and permitted assigns of each of the parties, provided that the parties shall not be permitted to assign any of their rights or obligations pursuant to this Agreement without the prior written consent of the other. Any attempted assignment by any party in violation of the foregoing shall be null and void.

(c) Entire Agreement; Amendment and Waiver. This Agreement constitutes the entire understanding of the parties hereto and supersedes all prior agreements or understandings with respect to the subject matter hereof among such parties. This Agreement may be amended, and the observance of any term of this Agreement may be waived, with (and only with) the written consent of all parties hereto.

(d) Severability. In the event that any part or parts of this Agreement shall be held illegal or unenforceable by any court or administrative body of competent jurisdiction, such determination shall not affect the remaining provisions of this Agreement which shall remain in full force and effect.

(e) Further Assurances. In connection with this Agreement and the transactions contemplated hereby, the Investor shall execute and deliver any additional documents and instruments and perform any additional acts that the Company determines to be necessary or appropriate to effectuate and perform the provisions of this Agreement and those transactions.

(f) No Partnership. Nothing in this Agreement and no actions taken by the parties under this Agreement shall constitute a partnership, association or other co-operative entity between any of the parties or cause any party to be deemed the agent of any other party for any purpose.

(g) Specific Performance. It is hereby agreed and acknowledged that it will be impossible to measure in money the damages that would be suffered if the parties fail to comply with any of the obligations herein imposed on them and that, in the event of any such failure, an aggrieved Person will be irreparably damaged and will not have an adequate remedy at law. Any such party shall, therefore, be entitled (in addition to any other remedy to which such party may be entitled at law or in equity) to injunctive relief, including specific performance, to enforce such obligations, without the posting of any bond and if any action should be brought in equity to enforce any of the provisions of this Agreement, none of the parties hereto shall raise the defense that there is an adequate remedy at law.

(h) Third Party Beneficiaries. This Agreement does not create any rights, claims or benefits inuring to any Person that is not a party hereto, and it does not create or establish any third party beneficiary hereto.

(i) Counterparts. This Agreement may be executed in two or more counterparts (including by facsimile), each of which shall be deemed an original and all of which together shall be considered one and the same agreement.

(j) After Acquired Securities. The Investor agrees that, except as otherwise provided herein, all of the provisions of this Agreement shall apply to all Securities and any

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Ordinary Shares or other securities of the Company now owned or hereafter issued to or acquired by the Investor in consequence of any exchange or reclassification of the Securities, corporate reorganization, or any other form of recapitalization, consolidation, acquisition, stock split or stock dividend.

(k) 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.

(l) Terms Generally. The words “hereby”, “herein”, “hereof”, “hereunder” and words of similar import refer to this Agreement as a whole and not merely to the specific section, paragraph or clause in which such word appears. All references herein to Articles and Sections shall be deemed references to Articles and Sections of this Agreement unless the context shall otherwise require. The words “include”, “includes” and “including” shall be deemed to be followed by the phrase “without limitation”. The definitions given for terms in this Agreement shall apply equally to both the singular and plural forms of the terms defined. References herein to any agreement or letter shall be deemed references to such agreement or letter as it may be amended, restated or otherwise revised from time to time. Whenever required by the context hereof, the singular number shall include the plural, and vice versa; the masculine gender shall include the feminine and neuter genders; and the neuter gender shall include the masculine and feminine genders.

(m) Draftsmanship. Each of the parties signing this Agreement on the date first set forth above has been represented by his or its own counsel and acknowledges that he or it has participated in the drafting of this Agreement, and any applicable rule of construction to the effect that ambiguities are to be resolved against the drafting party shall not be applied in connection with the construction or interpretation of this Agreement. Each of the parties joining this Agreement after the date first set forth above has been represented by his or its own counsel, has read and understands the terms of this Agreement and has been afforded the opportunity to ask questions concerning the Company and this Agreement, and any applicable rule of construction to the effect that ambiguities are to be resolved against the drafting party shall not be applied in connection with the construction or interpretation of this Agreement.

(n) Termination. This Agreement shall terminate and be of no further force or effect upon either party upon the later to occur of (i) the Transfer Restriction Termination Date or (ii) the end of the Standstill Period.

[Remainder of Page Intentionally Left Blank]

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

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: ***@***