RESTRICTED STOCK PROGRAM May 8, 2012 OFF CYCLE AWARD AGREEMENT

Exhibit 10.7

RESTRICTED STOCK PROGRAM

May 8, 2012

OFF CYCLE AWARD AGREEMENT

Employee Name:

ID Number:

Payroll Country: United States of America

Number of Restricted Stock Units Granted:

Grant Date: May 8, 2012

Grant Price: $53.61

Vesting Schedule: The restrictions lapse and the units vest on the third anniversary of the Grant Date.

Further Terms and Conditions

This Key Employee Award Terms and Conditions describes terms and conditions of Restricted Stock or Restricted Stock Unit Awards, as part of the ConocoPhillips Restricted Stock Program (Program), granted under the 2011 Omnibus Stock and Performance Incentive Plan of ConocoPhillips (referred to as the Plan) by ConocoPhillips (Company) to certain eligible Employees (Employees). These Terms and Conditions, together with the Annual Award Summary given to each Employee receiving an Award, form the Award Agreement (the Agreement) relating to the Awards described. The Agreement covers both Restricted Stock and Restricted Stock Units, and the term Employee covers recipients of Awards made either in Restricted Stock or Restricted Stock Units.

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Summary Table

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DEFINITIONS

Capitalized terms not defined below shall have the meanings set forth in the Plan.

Authorized Party means the person who is authorized to approve an Award, exercise discretion or take action under the Administrative Procedure for the Restricted Stock Program and pursuant to the Program. With regard to Senior Officers, the Committee is the Authorized Party. With regard to other Employees, the Chief Executive Officer, acting as the Special Equity Award Committee of the Board of Directors of the Company, is the Authorized Party, although the Committee may act concurrently as the Authorized Party.

Award means any Restricted Stock or Restricted Stock Units granted to an Employee pursuant to such applicable terms, conditions, and limitations as the Authorized Party may establish in order to fulfill the objectives of the Program.

Change of Control has the meaning set forth in Attachment A to these Terms and Conditions.

Committee means the Human Resources and Compensation Committee of the Board of Directors of the Company, or any successor committee to it.

Company means ConocoPhillips, a Delaware corporation.

Disability means a disability for which the employee in question has been determined to be entitled to either (i) benefits under the applicable plan of long-term disability of the Company or its subsidiaries or (ii) disability benefits under the Social Security Act. In the absence of any such determination, the Authorized Party may make a determination that the employee has a Disability.

Fair Market Value means, as of a particular date, the mean between the highest and lowest sales price per share of such Stock on the consolidated transaction reporting system for the principal national securities exchange on which shares of Stock are listed on that date, or, if there shall have been no such sale so reported on that date, on the next preceding date on which such a sale was so reported, or, at the discretion of the Committee, the price prevailing on the exchange at a designated time.

Grant Price means the Fair Market Value for one share of Stock as of the date of the grant of an Award. Grant price is not adjusted for any restrictions applicable to the Award.

Layoff means an applicable Termination of Employment due to layoff under the ConocoPhillips Severance Pay Plan, the ConocoPhillips Executive Severance Plan, or the ConocoPhillips Key Employee Change in Control Severance Plan, or layoff or redundancy under any similar layoff or redundancy plan which the Company or its subsidiaries may adopt from time to time. If all or any portion of the benefits under the redundancy or layoff plan are contingent on the employee’s signing a general release of liability, such Termination shall not be considered as a “Layoff” for purposes of this Award unless the employee executes and does not revoke a general release of liability, acceptable to the Company, under the terms of such layoff or redundancy plan. In order to be considered a layoff for purposes of this Award, the Termination of Employment must also be considered a Separation from Service.

Participating Company includes ConocoPhillips and its 100% owned subsidiaries, including both those directly owned and those owned through subsidiaries, whose participation has been approved by the Authorized Party.

Restricted Stock means shares of Stock that have certain restrictions attached to the ownership thereof.

Restricted Stock Unit means a unit equal to one share of Stock (as determined by the Authorized Party) that is subject to forfeiture provisions or that has certain restrictions attached to the ownership thereof.

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Retirement means Termination at age 55 or older with a minimum of 5 years service with a Participating Company; provided, however, that with regard to an Employee not on the United States payroll, the CEO may approve the use of a different definition. Service is defined by the policies of the Participating Company.

Senior Officer means the Chairman of the Board, the CEO, all other executive officers of the Company (determined in accordance with the Company’s custom and practice pursuant to section 16(b) of the Securities Exchange Act of 1934, as amended), all other employees of the Company who report directly to the CEO and whose salary grade is 23 or higher, and all other employees of the Company whose salary grade is 26 or higher.

Separation from Service means “separation from service” as that term is used in section 409A of the Internal Revenue Code.

Stock means shares of common stock of the Company, par value $.01. Stock may also be referred to as “Common Stock.”

Termination and Termination of Employment mean cessation of employment with the Participating Companies, determined in accordance with the policies and practices of the Participating Company for whom the Employee was last performing services.

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Exhibit 10.7

Attachment A

Change of Control

The following definitions apply to the Change of Control provision in Paragraph 10 of the Plan.

Affiliate shall have the meaning ascribed to such term in Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as in effect at the time of determination.

Associate shall mean, with reference to any Person, (a) any corporation, firm, partnership, association, unincorporated organization or other entity (other than the Company or a subsidiary of the Company) of which such Person is an officer or general partner (or officer or general partner of a general partner) or is, directly or indirectly, the Beneficial Owner of 10% or more of any class of equity securities, (b) any trust or other estate in which such Person has a substantial beneficial interest or as to which such Person serves as trustee or in a similar fiduciary capacity and (c) any relative or spouse of such Person, or any relative of such spouse, who has the same home as such Person.

Beneficial Owner shall mean, with reference to any securities, any Person if:

(a) such Person or any of such Person’s Affiliates and Associates, directly or indirectly, is the “Beneficial Owner” of (as determined pursuant to Rule 13d-3 of the General Rules and Regulations under the Exchange Act, as in effect at the time of determination) such securities or otherwise has the right to vote or dispose of such securities;

(b) such Person or any of such Person’s Affiliates and Associates, directly or indirectly, has the right or obligation to acquire such securities (whether such right or obligation is exercisable or effective immediately or only after the passage of time or the occurrence of an event) pursuant to any agreement, arrangement or understanding (whether or not in writing) or upon the exercise of conversion rights, exchange rights, other rights, warrants or options, or otherwise; provided, however, that a Person shall not be deemed the Beneficial Owner of, or to “beneficially own,” (i) securities tendered pursuant to a tender or exchange offer made by such Person or any of such Person’s Affiliates or Associates until such tendered securities are accepted for purchase or exchange or (ii) securities issuable upon exercise of Exempt Rights; or

(c) such Person or any of such Person’s Affiliates or Associates (i) has any agreement, arrangement or understanding (whether or not in writing) with any other Person (or any Affiliate or Associate thereof) that beneficially owns such securities for the purpose of acquiring, holding, voting (except as set forth in the proviso to subsection (a) of this definition) or disposing of such securities or (ii) is a member of a group (as that term is used in Rule 13d-5(b) of the General Rules and Regulations under the Exchange Act) that includes any other Person that beneficially owns such securities;

provided, however, that nothing in this definition shall cause a Person engaged in business as an underwriter of securities to be the Beneficial Owner of, or to beneficially own, any securities acquired through such Person’s participation in good faith in a firm commitment underwriting until the expiration of 40 days after the date of such acquisition. For purposes hereof, “voting” a security shall include voting, granting a proxy, consenting or making a request or demand relating to corporate action (including, without limitation, a demand for a shareholder list, to call a shareholder meeting or to inspect corporate books and records) or otherwise giving an authorization (within the meaning of Section 14(a) of the Exchange Act) in respect of such security.

The terms beneficially own and beneficially owning shall have meanings that are correlative to this definition of the term Beneficial Owner.

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Board shall have the meaning set forth in the foregoing Plan.

Change of Control shall mean any of the following occurring on or after May 11, 2011:

(a) any Person (other than an Exempt Person) shall become the Beneficial Owner of 20% or more of the shares of Common Stock then outstanding or 20% or more of the combined voting power of the Voting Stock of the Company then outstanding; provided, however, that no Change of Control shall be deemed to occur for purposes of this subsection (a) if such Person shall become a Beneficial Owner of 20% or more of the shares of Common Stock or 20% or more of the combined voting power of the Voting Stock of the Company solely as a result of (i) an Exempt Transaction or (ii) an acquisition by a Person pursuant to a reorganization, merger or consolidation, if, following such reorganization, merger or consolidation, the conditions described in clauses (i), (ii) and (iii) of subsection (c) of this definition are satisfied;

(b) individuals who, as of May 11, 2011, constitute the Board (the “Incumbent Board”) cease for any reason to constitute at least a majority of the Board; provided, however, that any individual becoming a director subsequent to May 11, 2011 whose election, or nomination for election by the Company’s shareholders, was approved by a vote of at least a majority of the directors then comprising the Incumbent Board shall be considered as though such individual were a member of the Incumbent Board; provided, further, that there shall be excluded, for this purpose, any such individual whose initial assumption of office occurs as a result of any actual or threatened Election Contest that is subject to the provisions of Rule 14a-11 of the General Rules and Regulations under the Exchange Act;

(c) the Company shall consummate a reorganization, merger, or consolidation, in each case, unless, following such reorganization, merger, or consolidation, (i) 50% or more of the then outstanding shares of common stock of the corporation, or common equity securities of an entity other than a corporation, resulting from such reorganization, merger, or consolidation and the combined voting power of the then outstanding Voting Stock of such corporation or other entity are beneficially owned, directly or indirectly, by all or substantially all of the Persons who were the Beneficial Owners of the outstanding Common Stock immediately prior to such reorganization, merger, or consolidation in substantially the same proportions as their ownership, immediately prior to such reorganization, merger, or consolidation, of the outstanding Common Stock, (ii) no Person (excluding any Exempt Person or any Person beneficially owning, immediately prior to such reorganization, merger, or consolidation, directly or indirectly, 20% or more of the Common Stock then outstanding or 20% or more of the combined voting power of the Voting Stock of the Company then outstanding) beneficially owns, directly or indirectly, 20% or more of the then outstanding shares of common stock of the corporation, or common equity securities of an entity other than a corporation, resulting from such reorganization, merger, or consolidation or the combined voting power of the then outstanding Voting Stock of such corporation or other entity, and (iii) at least a majority of the members of the board of directors of the corporation, or the body which is most analogous to the board of directors of a corporation if not a corporation, resulting from such reorganization, merger, or consolidation were members of the Incumbent Board at the time of the initial agreement or initial action by the Board providing for such reorganization, merger, or consolidation; or

(d) (i) the shareholders of the Company shall approve a complete liquidation or dissolution of the Company unless such liquidation or dissolution is approved as part of a plan of liquidation and dissolution involving a sale or disposition of all or substantially all of the assets of the Company to a corporation with respect to which, following such sale or other disposition, all of the requirements of clauses (ii)(A), (B), and (C) of this subsection (d) are satisfied, or (ii) the Company shall consummate the sale or other disposition of all or substantially all of the assets of the Company, other than to a corporation or other entity, with respect to which, following such sale or other disposition, (A) 50% or more of the then outstanding shares of common stock of such corporation, or common

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equity securities of an entity other than a corporation, and the combined voting power of the Voting Stock of such corporation or other entity is then beneficially owned, directly or indirectly, by all or substantially all of the Persons who were the Beneficial Owners of the outstanding Common Stock immediately prior to such sale or other disposition in substantially the same proportion as their ownership, immediately prior to such sale or other disposition, of the outstanding Common Stock, (B) no Person (excluding any Exempt Person and any Person beneficially owning, immediately prior to such sale or other disposition, directly or indirectly, 20% or more of the Common Stock then outstanding or 20% or more of the combined voting power of the Voting Stock of the Company then outstanding) beneficially owns, directly or indirectly, 20% or more of the then outstanding shares of common stock of such corporation, or common equity securities of an entity other than a corporation, and the combined voting power of the then outstanding Voting Stock of such corporation or other entity, and (C) at least a majority of the members of the board of directors of such corporation, or the body which is most analogous to the board of directors of a corporation if not a corporation, were members of the Incumbent Board at the time of the initial agreement or initial action of the Board providing for such sale or other disposition of assets of the Company.

Common Stock shall have the meaning set forth in the foregoing Plan.

Company shall have the meaning set forth in the foregoing Plan.

Election Contest shall mean a solicitation of proxies of the kind described in Rule 14a-12(c) under the Exchange Act.

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

Exempt Person shall mean any of the Company, any subsidiary of the Company, any employee benefit plan of the Company or any subsidiary of the Company, and any Person organized, appointed or established by the Company for or pursuant to the terms of any such plan.

Exempt Rights shall mean any rights to purchase shares of Common Stock or other Voting Stock of the Company if at the time of the issuance thereof such rights are not separable from such Common Stock or other Voting Stock (i.e., are not transferable otherwise than in connection with a transfer of the underlying Common Stock or other Voting Stock), except upon the occurrence of a contingency, whether such rights exist as of May 11, 2011 or are thereafter issued by the Company as a dividend on shares of Common Stock or other Voting Securities or otherwise.

Exempt Transaction shall mean an increase in the percentage of the outstanding shares of Common Stock or the percentage of the combined voting power of the outstanding Voting Stock of the Company beneficially owned by any Person solely as a result of a reduction in the number of shares of Common Stock then outstanding due to the repurchase of Common Stock or Voting Stock by the Company, unless and until such time as (a) such Person or any Affiliate or Associate of such Person shall purchase or otherwise become the Beneficial Owner of additional shares of Common Stock constituting 1% or more of the then outstanding shares of Common Stock or additional Voting Stock representing 1% or more of the combined voting power of the then outstanding Voting Stock, or (b) any other Person (or Persons) who is (or collectively are) the Beneficial Owner of shares of Common Stock constituting 1% or more of the then outstanding shares of Common Stock or Voting Stock representing 1% or more of the combined voting power of the then outstanding Voting Stock shall become an Affiliate or Associate of such Person.

Person shall mean any individual, firm, corporation, partnership, association, trust, unincorporated organization or other entity.

Voting Stock shall mean, (1) with respect to a corporation, all securities of such corporation of any class or series that are entitled to vote generally in the election of, or to appoint by contract, directors

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of such corporation (excluding any class or series that would be entitled so to vote by reason of the occurrence of any contingency, so long as such contingency has not occurred) and (ii) with respect to an entity which is not a corporation, all securities of any class or series that are entitled to vote generally in the election of, or to appoint by contract, members of the body which is most analogous to the board of directors of a corporation.

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