EATON VANCE TAX-MANAGED BUY-WRITE OPPORTUNITIES FUND AMENDED AND RESTATED ADMINISTRATIVE SERVICES AGREEMENT

EXHIBIT (k)(4)

▇▇▇▇▇ ▇▇▇▇▇ TAX-MANAGED BUY-WRITE OPPORTUNITIES FUND

AMENDED AND RESTATED ADMINISTRATIVE SERVICES AGREEMENT

AGREEMENT made this 6th day of August, 2012, between ▇▇▇▇▇ ▇▇▇▇▇ Tax-Managed Buy-Write Opportunities Fund, a Massachusetts business trust (the “Fund”), and ▇▇▇▇▇ ▇▇▇▇▇ Management, a Massachusetts business trust (the “Administrator”).

1. Duties of the Administrator. The Fund hereby employs the Administrator to act as administrator for and to administer the affairs of the Fund, subject to the supervision of the Trustees of the Fund for the period and on the terms set forth in this Agreement.

The Administrator hereby accepts such employment, and agrees to administer the Fund’s business affairs and, in connection therewith, to furnish for the use of the Fund office space and all necessary office facilities, equipment and personnel for administering the affairs of the Fund. The Administrator shall also pay the salaries and compensation of all officers and Trustees of the Fund who are members of the Administrator’s organization and who render executive and administrative services to the Fund, and the salaries and compensation of all other personnel of the Administrator performing management and administrative services for the Fund. The Administrator shall for all purposes herein be deemed to be an independent contractor and shall, except as otherwise expressly provided or authorized, have no authority to act for or represent the Fund in any way or otherwise be deemed an agent of the Fund.

In connection with its responsibilities as Administrator of the Fund, the Administrator will:

assist in preparing all annual, semi-annual and other reports required to be sent to Fund shareholders and/or with the Securities and Exchange Commission (“SEC”), and arrange for the printing and dissemination of such reports to shareholders;

prepare and assemble all reports required to be filed by the Fund with the SEC on Forms N-SAR, or on such other form as the SEC may substitute for Form N-SAR, and file such reports with the SEC;

review the provision of services by the Fund’s independent accountants, including, but not limited to, the preparation by such firm of audited financial statements of the Fund and the Fund’s federal, state and local tax returns; and make such reports and recommendations to the Trustees of the Fund concerning the performance of the independent accountants as the Trustees deem appropriate;

arrange for the filing with the appropriate authorities all required federal, state and local tax returns;

arrange for the dissemination to shareholders of the Fund’s proxy materials, and oversee the tabulation of proxies by the Fund’s transfer agent or other duly authorized proxy tabulator;

review and supervise the provision of custodian services to the Fund; and make such reports and recommendations to the Trustees concerning the provision of such services as the Trustees deem appropriate;

oversee the valuation of all such portfolio investments and other assets of the Fund as may be designated by the Trustees (subject to any guidelines, directions and instructions of the Trustees), and review and supervise the calculation of the net asset value of the Fund’s shares by the custodian;

negotiate the terms and conditions under which transfer agency and dividend disbursing services will be provided to the Fund, and the fees to be paid by the Fund in connection therewith; review and supervise the provision of transfer agency and dividend disbursing services to the Fund; and make such reports and recommendations to the Trustees concerning the performance of the Fund’s transfer and dividend disbursing agent as the Trustees deem appropriate;

establish the accounting policies of the Fund; reconcile accounting issues which may arise with respect to the Fund’s operations; and consult with the Fund’s independent accountants, legal counsel, custodian, accounting and bookkeeping agents and transfer and dividend disbursing agent as necessary in connection therewith;

determine the amount of all distributions (if any) to be paid by the Fund to its shareholders; prepare and arrange for the publishing of notices to shareholders regarding such distributions (if required) and provide the Fund’s transfer and dividend disbursing agent and custodian with such information as is required for such parties to effect the payment of distributions and to implement the Fund’s dividend reinvestment plan;

review the Fund’s bills and authorize payments of such bills by the Fund’s custodian;

oversee services provided to the Fund by external counsel;

make recommendations to the Trustees as to whether the Fund should make repurchase or tender offers for its own shares; arrange for the preparation and filing of all documents required to be filed by the Fund with the SEC; arrange for the preparation and dissemination of all appropriate repurchase or tender offer documents and papers on behalf of the Fund; and supervise and conduct the Fund’s periodic repurchase or tender offers for its own shares;

monitor any variance between the market value and net asset value per share, and periodically report to the Trustees available actions that may conform such values;

monitor the activities of any shareholder servicing agent retained by the Administrator and periodically report to the Trustees about such activities;

arrange for the preparation and filing of all other reports, forms, registration statements and documents required to be filed by the Fund with the SEC, the Financial Industry Regulatory Authority and any securities exchange where Fund shares are listed; and

provide other internal legal, auditing, accounting and administrative services as ordinarily required in conducting the Fund’s business affairs.

Notwithstanding the foregoing, the Administrator shall not be deemed to have assumed any duties with respect to, and shall not be responsible for, the management of the Fund’s assets or the rendering of investment advice and supervision with respect thereto or the distribution of shares of the Fund, nor shall the Administrator be deemed to have assumed or have any responsibility with respect to functions specifically assumed by any transfer agent, custodian or shareholder servicing agent of the Fund.

Sub-Administrators. The Administrator may employ one or more sub-administrators from time to time to perform such of the acts and services of the Administrator and upon such terms and conditions as may be agreed upon between the Administrator and such sub-administrators and approved by the Trustees of the Fund, all as permitted by the Investment Company Act of 1940.

Compensation of the Administrator. The Board of Trustees of the Fund have currently determined that, based on the current level of compensation payable to ▇▇▇▇▇ ▇▇▇▇▇ Management by the Fund under the Fund’s present Investment Advisory Agreement with ▇▇▇▇▇ ▇▇▇▇▇ Management, the Administrator shall receive no compensation from the Fund in respect of the services to be rendered and the facilities to be provided by the Administrator under this Agreement. If the Trustees subsequently determine that the Fund should compensate the Administrator for such services and facilities, such compensation shall be set forth in a new agreement or in an amendment to this Agreement to be entered into by the parties hereto.

Allocation of Charges and Expenses. It is understood that the Fund will pay all its expenses other than those expressly stated to be payable by the Administrator hereunder, which expenses payable by the Fund shall include, without implied limitation:

expenses of maintaining the Fund and continuing its existence;

commissions, fees and other expenses connected with the acquisition and disposition of securities and other investments;

auditing, accounting and legal expenses;

taxes and interest;

governmental fees;

expenses of repurchase and redemption (if any) of shares, including all expenses incurred in conducting repurchase and tender offers for the purpose of repurchasing Fund shares;

expenses of registering and qualifying the Fund and its shares under federal and state securities laws and of preparing registration statements and amendments for such purposes, and fees and expenses of registering and maintaining registrations of the Fund under state securities laws;

registration of the Fund under the Investment Company Act of 1940;

expenses of reports and notices to shareholders and of meetings of shareholders and proxy solicitations therefor;

expenses of reports to regulatory bodies;

insurance expenses;

association membership dues;

fees, expenses and disbursements of custodians and subcustodians for all services to the Fund (including without limitation safekeeping of funds, securities and other investments, keeping of books and accounts and determination of net asset values);

fees, expenses and disbursements of transfer agents, dividend disbursing agents, shareholder servicing agents and registrars for all services to the Fund;

expenses of listing shares with a stock exchange;

any direct charges to shareholders approved by the Trustees of the Fund;

compensation and expenses of Trustees of the Fund who are not members of the Administrator’s organization;

all payments to be made and expenses to be assumed by the Fund in connection with the distribution of Fund shares;

any pricing and valuation services employed by the Fund to value its investments including primary and comparative valuation services;

any investment advisory, sub-advisory or similar management fee payable by the Fund;

all expenses incurred in connection with the Fund’s use of a line of credit, or issuing and maintaining preferred shares; and

such non-recurring items as may arise, including expenses incurred in connection with litigation, proceedings and claims and the obligation of the Fund to indemnify its Trustees and officers with respect thereto.

Other Interests. It is understood that Trustees, officers and shareholders of the Fund are or may be or become interested in the Administrator as trustees, officers, employees, shareholders or otherwise and that trustees, officers, employees and shareholders of the Administrator are or may be or become similarly interested in the Fund, and that the Administrator may be or become interested in the Fund as a shareholder or otherwise. It is also understood that trustees, officers, employees and shareholders of the Administrator may be or become interested (as directors, trustees, officers, employees, shareholders or otherwise) in other companies or entities (including, without limitation, other investment companies) that the Administrator may organize, sponsor or acquire, or with which it may merge or consolidate, and which may include the words “▇▇▇▇▇ ▇▇▇▇▇” or any combination thereof as part of their name, and that the Administrator or its subsidiaries or affiliates may enter into advisory or management or administration agreements or other contracts or relationship with such other companies or entities.

Limitation of Liability of the Administrator. The services of the Administrator to the Fund are not to be deemed to be exclusive, the Administrator being free to render services to others and engage in other business activities. In the absence of willful misfeasance, bad faith, gross negligence or reckless disregard of obligations or duties hereunder on the part of the Administrator, the Administrator shall not be subject to liability to the Fund or to any shareholder of the Fund for any act or omission in the course of, or connected with, rendering services hereunder or for any losses which may be sustained in the acquisition, holding or disposition of any security or other investment.

Duration and Termination of this Agreement. This Agreement shall become effective upon the date of its execution, and, unless terminated as herein provided, shall remain in full force and effect through and including the second anniversary of the execution of this Agreement and shall continue in full force and effect indefinitely thereafter, but only so long as such continuance after such date is specifically approved at least annually (i) by the Board of Trustees of the Fund and (ii) by the vote of a majority of those Trustees of the Fund who are not interested persons of the Administrator or the Fund.

Either party hereto may, at any time on sixty (60) days’ prior written notice to the other, terminate this Agreement without the payment of any penalty, by action of the Trustees of the Fund or the trustee of the Administrator, as the case may be, and the Fund may, at any time upon such written notice to the Administrator, terminate the Agreement by vote of a majority of the outstanding voting securities of the Fund. This Agreement shall terminate automatically in the event of its assignment.

Amendments of the Agreement. This Agreement may be amended by a writing signed by both parties hereto, provided that no amendment to this Agreement shall be effective until approved (i) by the vote of a majority of those Trustees of the Fund who are not interested persons of the Administrator or the Fund, and (ii) by vote of the Board of Trustees of the Fund.

Limitation of Liability. Each party expressly acknowledges the provision in the other party’s Agreement and Declaration of Trust limiting the personal liability of trustees, officers and shareholders, and each party hereby agrees that it shall only have recourse to the assets of the other party for payment of claims or obligations arising out of this Agreement and shall not seek satisfaction from the Trustees, officers or shareholders of the other party.

Use of the Name “▇▇▇▇▇ ▇▇▇▇▇.” The Administrator hereby consents to the use by the Fund of the name “▇▇▇▇▇ ▇▇▇▇▇” as part of the Fund’s name; provided, however, that such consent shall be conditioned upon the employment of the Administrator or one of its affiliates as the administrator of the Fund. The name “▇▇▇▇▇ ▇▇▇▇▇” or any variation thereof may be used from time to time in other connections and for other purposes by the Administrator and its affiliates and other investment companies that have obtained consent to the use of the name “▇▇▇▇▇ ▇▇▇▇▇.” The Administrator shall have the right to require the Fund to cease using the name “▇▇▇▇▇ ▇▇▇▇▇” as part of the Fund’s name if the Fund ceases, for any reason, to employ the Administrator or one of its affiliates as the Fund’s administrator. Future names adopted by the Fund for itself, insofar as such names include identifying words requiring the consent of the Administrator, shall be the property of the Administrator and shall be subject to the same terms and conditions.

10.

Certain Definitions. The terms “assignment” and “interested persons” when used herein shall have the respective meanings specified in the Investment Company Act of 1940 as now in effect or as hereafter amended subject, however, to such exemptions as may be granted by the Securities and Exchange Commission by any rule, regulation or order. The term “vote of a majority of the outstanding voting securities” shall mean the vote of the lesser of (a) 67 per centum or more of the shares of the Fund present or represented by proxy at the meeting if the holders of more than 50 per centum of the outstanding shares of the Fund are present or represented by proxy at the meeting, or (b) more than 50 per centum of the outstanding shares of the Fund.

IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be executed on the day and year first above written.

▇▇▇▇▇ ▇▇▇▇▇ TAX-MANAGED BUY-WRITE

▇▇▇▇▇ ▇▇▇▇▇ MANAGEMENT

OPPORTUNITIES FUND

By:

/s/ ▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇

By:

/s/ ▇▇▇▇▇▇▇ ▇. Gemma

▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇

▇▇▇▇▇▇▇ ▇. Gemma

Assistant Treasurer

Vice President

EATON VANCE TAX-MANAGED BUY-WRITE OPPORTUNITIES FUND AMENDED AND RESTATED ADMINISTRATIVE SERVICES AGREEMENT

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