PERFORMANCE AWARD AGREEMENT UNDER THE TEXAS CAPITALBANCSHARES, INC. 2010 LONG-TERM INCENTIVE PLAN

Exhibit 10.3

PERFORMANCE AWARD AGREEMENT

UNDER THE

TEXAS CAPITAL BANCSHARES, INC.

2010 LONG-TERM INCENTIVE PLAN

1. Award of Performance Units. Pursuant to the Texas Capital Bancshares, Inc. 2010 Long-Term Incentive Plan (the “Plan”) of Texas Capital Bancshares, Inc., a Delaware corporation (the “Company”) and its Subsidiaries,

George Jones

(the “Participant”)

as an employee of the Company, has been granted an Award under the Plan for 30,000 Performance Units (the “Awarded Units”), which shall be converted into a cash payment equal to the Value (as determined under Section 4 below) of the number of vested Performance Units (determined in accordance with Section 3 below), subject to the terms and conditions of the Plan and this Performance Award Agreement (this “Agreement”). The Date of Grant of this Award is December 18, 2013. Each Awarded Unit shall be a notional share of Common Stock, and shall not entitle the Participant to receive any shares of Common Stock at any time. The grant of the Awarded Units is subject to and conditioned upon, the execution and delivery by the Participant of the Waiver and Release of Claims attached as Exhibit A (the “Release”) to that certain Retirement Transition Agreement and Release dated June 11, 2013 by and between the Participant and the Company (the “Transition Agreement”). In the event the Participant fails to timely execute and deliver the Release, or revokes the Release, one hundred percent (100%) of the Awarded Units shall be immediately forfeited, and no Value (as defined in Section 4 below) shall be paid or due with respect to such forfeited Awarded Units.

2. Subject to Plan. This Agreement is subject to the terms and conditions of the Plan, and the terms of the Plan shall control to the extent inconsistent with the provisions of this Agreement. The capitalized terms used herein that are defined in the Plan shall have the same meanings assigned to them in the Plan, except as otherwise expressly provided herein. This Agreement is subject to any rules promulgated pursuant to the Plan by the Board or the Committee and communicated to the Participant in writing.

3. Vesting. Awarded Units which have become vested pursuant to the terms of this Section 3 are collectively referred to herein as “Vested Units.” All other Awarded Units are collectively referred to herein as “Unvested Units.” The Participant shall be eligible to receive payment with respect to the Vested Units in accordance with Section 4 below.

a. Subject to the provisions of Section 5 below and except as otherwise provided in this Section 3:

(i) Forty percent (40%) of the Awarded Units shall become Vested Units on February 15, 2018; and

(ii) Sixty percent (60%) of the Awarded Units shall vest in accordance with the performance metrics established for equity awards granted to the senior executives of the Company in 2015, as determined by the Board in its sole discretion. Notwithstanding the foregoing, when establishing the performance objectives applicable to the Awarded Units that eligible for vesting in accordance with this Section 3.a.(ii), the Board shall not treat the Participant less favorably than the Company’s then Chief Executive Officer or Chief Financial Officer.

b. Notwithstanding the foregoing, all Unvested Units shall immediately become Vested Units:

(i) upon the Participant’s death or Total and Permanent Disability;

(ii) on the effective date of a Change in Control; or

(iii) on any date prior to the Separation Date that the Participant’s employment with the Company is terminated by the Company without Cause (as defined in the Executive Employment Agreement by and between the Company and the Participant, effective as of December 31, 2008 (the “Employment Agreement”)).

4. Payment with Respect to Vested Units. The Value of each Vested Unit shall be payable in accordance with the following schedule, provided that the Participant has not violated the Surviving Provisions (as defined in the Transition Agreement) prior to such date:

a. if vested pursuant to Section 3.a.(ii), as soon as administratively practicable following determination by the Committee that the vesting conditions applicable to such Vested Units have been achieved; or

b. if vested pursuant to Section 3.a.(i). or Section 3.b., within thirty (30) days following the date on which the Awarded Units become Vested Units in accordance with said Sections.

To the extent an Awarded Unit does not vest in accordance with the provisions of Section 3(a)(ii) or Section 3(b) hereof by 2018, such Awarded Unit shall be forfeited and no Value shall be paid or due with respect to such forfeited Awarded Unit. For purposes of this Agreement, the “Value” shall mean the average closing price per share of the Company’s Common Stock during the twenty (20) consecutive trading days before December 31, 2017, multiplied by the number of vested Performance Units; provided, however, that upon a Change in Control, the Value shall mean the number of Performance Units set forth in Section 1 above (regardless of whether such units are vested) multiplied by (i) with respect to a Change in Control where the consideration received by the stockholders or the Company is cash, the actual consideration paid to the stockholders per share of Common Stock; (ii) with respect to any Change in Control where the consideration received by the stockholders or the Company is equity of the acquiring entity, the average closing price per share of the Company’s Common Stock during the twenty (20) consecutive trading days immediately prior to the effective time of the Change in Control; or (iii) with respect to any Change in Control where the consideration received by the stockholders or the Company is a combination of cash and equity, a combination of (i) and (ii), determined based upon the proportion of the aggregate consideration received that is cash versus equity. Notwithstanding anything to the contrary contained herein, the Value that shall be eligible for payout with respect to Awarded Units that vest in accordance with Section 3.a.(ii) hereof shall be subject to adjustment in the same manner, and to the same extent, as the performance equity awards granted to the senior executives in 2015 are subject to adjustment.

5. Forfeiture and Disgorgement.

a. Notwithstanding any provisions in this Agreement to the contrary, in the event the Participant violates the Surviving Provisions (as defined in the Transition Agreement), or the provisions of any agreement between the Company (or any of its Subsidiaries) that contains confidentiality, non-solicitation or other protective or restrictive covenant provisions, then:

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(i) the Awarded Units shall immediately cease to vest as of the date of such violation;

(ii) any Value that had not been paid with respect to Awarded Units shall be immediately forfeited and this Agreement (other than the provisions of this Section 5) will be terminated on the date of such violation; and

(iii) any Value (less any taxes paid by the Participant on such Value) that had been paid to the Participant with respect to any Vested Units shall be immediately paid to the Company by the Participant.

The Company must deliver written notice of its intent to enforce the provisions of this Section 5.a. at least fifteen (15) days prior to the date it intends to enforce the terms of Section 5.a.(i) and (ii). If the Participant desires to oppose the Company’s enforcement of this Section 5.a., then the Participant must request that the dispute be submitted to binding arbitration in accordance with the provisions of Section 5.b. below. Both the Company and the Participant agree that upon delivery of written notice under this Section 5.a., neither party will enter into any transaction that will affect the other party’s interests in the cash subject to dispute until the later of (i) the expiration of the fifteen (15) day notice period or (ii) if the Participant requests arbitration, resolution of the arbitration proceedings. The parties further agree that upon commencement of any arbitration proceedings, the parties shall transfer any cash that is the subject of the dispute to an escrow agent, who shall hold such cash in trust until the resolution of the arbitration proceedings.

The provisions of this Section 5 (including, without limitation, the provisions of this Section 5.a., and the provisions of Section 5.b. below) only shall apply to the Awarded Units for the period beginning on the Date of Grant and ending on the one year anniversary of the date the Awarded Units become vested in accordance with the provisions of Section 3 above (regardless of whether the Agreement terminates or expires prior to such date).

b. If any dispute between the Participant and the Company arises out of this Section 5, and the Participant and the Company cannot resolve the dispute, the Participant and the Company agree to submit the dispute to final and binding arbitration. Arbitration of any disputes arising out of this Section 5 is mandatory and in lieu of all civil causes of action or lawsuits either party may have against the other arising under Section 5. The arbitration will be conducted in accordance with the American Arbitration Association’s (“AAA”) National Rules for the Resolution of Employment Disputes (“Rules”). If the Participant and the Company cannot agree to an arbitrator, then they will select an arbitrator through the AAA’s standard procedures and Rules. The Company and the Participant will share equally the costs assessed and incurred by the arbitrator. The Company and the Participant agree that the arbitration of any dispute arising out of this Section 5 will be held in Dallas, Texas. The decision of the arbitrator shall be final and binding on all parties. This arbitration provision applies only to Section 5 of this Agreement and does not apply to any other word, sentence, paragraph or part of this Agreement.

6. Who May Receive Payments with Respect to Vested Units. During the lifetime of the Participant, the cash received upon payout of Vested Units may only be received by the Participant or his or her legal representative. If the Participant dies prior to the date payment is made with respect to his or her Vested Units as described in Section 3 above, payment relating to such Vested Units may be received by any individual who is entitled to receive the property of the Participant pursuant to the applicable laws of descent and distribution.

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7. Rights as Stockholder. The Participant will have no rights as a stockholder with respect to the Awarded Units. The Awarded Units shall be subject to the terms and conditions of this Agreement.

8. The Participant’s Acknowledgments. The Participant acknowledges receipt of a copy of the Plan, which is annexed hereto, and represents that he or she is familiar with the terms and provisions thereof, and hereby accepts the Awarded Units subject to all the terms and provisions thereof. The Participant hereby agrees to accept as binding, conclusive, and final all decisions or interpretations of the Committee or the Board, as appropriate, upon any questions arising under the Plan or this Agreement.

9. Execution of Documents. The Participant, by his or her execution of this Agreement, hereby agrees to execute any documents requested by the Company in connection with the payment of any amount in connection with the Awarded Units pursuant to this Agreement.

10. Remedies. Except as otherwise provided in Section 5 in this Agreement, each of the parties to this Agreement will be entitled to enforce its rights under this Agreement specifically, to recover damages and costs (including reasonable attorneys’ fees) caused by any breach of any provision of this Agreement, and to exercise all other rights existing in the party’s favor. The parties hereto agree and acknowledge that money damages may not be an adequate remedy for any breach of the provisions of this Agreement and that any party in its, his or her sole discretion may apply to any court of law or equity of competent jurisdiction (without posting any bond or deposit) (or with respect to disputes under Section 5, to an arbitrator) for specific performance and/or other injunctive relief in order to enforce or prevent any violations of the provisions of this Agreement. The remedies for any violation of Section 5 above are limited to the forfeiture, disgorgement, injunction and arbitration remedies specified in Sections 5.a. and b., and any remedies, including injunctive relief, as more specifically set forth in the Employment Agreement, and are subject to the time-limitations set forth in Section 5.a. above. The remedies described in this Section 10 do not apply to Section 5.

11. Law Governing. This Agreement shall be governed by, construed, and enforced in accordance with the laws of the State of Texas (excluding any conflict of laws rule or principle of Texas law that might refer the governance, construction, or interpretation of this agreement to the laws of another state).

12. No Right to Continue Service or Employment. Nothing herein shall be construed to confer upon the Participant the right to continue in the employ or to provide services to the Company or any Subsidiary, whether as an Employee, Contractor, Consultant or Outside Director, or interfere with or restrict in any way the right of the Company or any Subsidiary to discharge the Participant as an Employee, Contractor, Consultant or Outside Director at any time.

13. Legal Construction. In the event that any one or more of the terms, provisions, or agreements that are contained in this Agreement shall be held by a court of competent jurisdiction to be invalid, illegal, or unenforceable in any respect for any reason, the invalid, illegal, or unenforceable term, provision, or agreement shall not affect any other term, provision, or agreement that is contained in this Agreement and this Agreement shall be construed in all respects as if the invalid, illegal, or unenforceable term, provision, or agreement had never been contained herein.

14. Covenants and Agreements as Independent Agreements. Each of the covenants and agreements set forth in this Agreement shall be construed as a covenant and agreement independent of any other provision of this Agreement. The existence of any claim or cause of action of the Participant against the Company, whether predicated on this Agreement or otherwise, shall not constitute a defense to the enforcement by the Company of the covenants and agreements that are set forth in this Agreement.

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15. Entire Agreement. This Agreement, together with the Plan, the Surviving Provisions of the Employment Agreement, and the Transition Agreement, supersede any and all other prior understandings and agreements, either oral or in writing, between the parties with respect to the subject matter in this Agreement and constitute the only agreements between the parties with respect to the subject matter in this Agreement. Except for the Transition Agreement between the Participant and the Company, all prior negotiations and agreements between the parties with respect to the subject matter in this Agreement are merged into this Agreement. Each party to this Agreement acknowledges that no representations, inducements, promises, or agreements, orally or otherwise, have been made by any party or by anyone acting on behalf of any party, which are not embodied in this Agreement or the Plan and that any agreement, statement or promise that is not contained in this Agreement or the Plan shall not be valid or binding or of any force or effect.

16. Counterparts. This Agreement may be executed in separate counterparts, each of which shall be deemed to be an original and all of which taken together shall constitute one and the same agreement.

17. Parties Bound. The terms, provisions, and agreements that are contained in this Agreement shall apply to, be binding upon, and inure to the benefit of the parties and their respective heirs, executors, administrators, legal representatives, and permitted successors and assigns, subject to the limitation on assignment expressly set forth herein.

18. Modification. No change or modification of this Agreement shall be valid or binding upon the parties unless the change or modification is in writing and signed by the parties; provided, however, that the Company may change or modify this Agreement without the Participant’s consent or signature if the Company determines, in its sole discretion, that such change or modification is necessary for purposes of compliance with or exemption from the requirements of Section 409A of the Code or any regulations or other guidance issued thereunder.

19. Headings. The headings that are used in this Agreement are used for reference and convenience purposes only and do not constitute substantive matters to be considered in construing the terms and provisions of this Agreement.

20. Gender and Number. Words of any gender used in this Agreement shall be held and construed to include any other gender, and words in the singular number shall be held to include the plural, and vice versa, unless the context requires otherwise.

21. Notice. Any notice required or permitted to be delivered hereunder shall be deemed to be delivered only when actually received by the Company or by the Participant, as the case may be, at the addresses set forth below, or at such other addresses as they have theretofore specified by written notice delivered in accordance herewith:

a. Notice to the Company shall be addressed and delivered as follows:

Texas Capital Bancshares, Inc.

2000 McKinney Avenue, Suite 700

Dallas, Texas 75201

Attn: Human Resources

Facsimile: 214 ###-###-####

b. Notice to the Participant shall be addressed and delivered as set forth on the signature page.

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22. Tax Requirements. The Participant is hereby advised to consult immediately with his or her own tax advisor regarding the tax consequences of this Agreement, including, without limitation, any possible tax consequences of this Agreement in connection with Section 409A of the Code. Unless the Company otherwise consents in writing to an alternative withholding method, the Company, or if applicable, any Subsidiary (for purposes of this Section 22, the term “Company” shall be deemed to include any applicable Subsidiary) shall withhold the amount of any Federal, state, local, or other taxes required by law to be withheld in connection with this Award. The Company also may, in its sole discretion, withhold any such taxes from any other cash remuneration otherwise paid by the Company to the Participant.

23. Section 409A.

a. To the extent (i) any payment to which the Participant becomes entitled under this Agreement, or any agreement or plan referenced herein, in connection with the Participant’s termination of employment with the Company constitutes deferred compensation subject to Section 409A of the Code; (ii) the Participant is deemed at the time of his separation from service to be a “specified employee” under Section 409A of the Code; and (iii) at the time of the Participant’s separation from service the Company is publicly traded (as defined in Section 409A of the Code), then such payment or transfer (other than any payment or transfer permitted by Section 409A of the Code to be paid within six (6) months of the Participant’s separation from service) shall not be made until the earlier of (x) the first day of the seventh month following the Participant’s separation from service or (y) the date of the Participant’s death following such separation from service. During any period that a payment to the Participant is deferred pursuant to the foregoing, the Participant shall be entitled to interest on the deferred payment at a per annum rate equal to Federal-Funds rate as published in The Wall Street Journal on the date of the Participant’s termination of employment with the Company. Upon the expiration of the applicable deferral period, any payments which would have otherwise been made during that period (whether in a single sum or in installments) in the absence of this Section 23 (together with, as applicable, accrued interest thereon) shall be paid to the Participant or the Participant’s beneficiary in one lump sum.

b. A termination of employment shall not be deemed to have occurred for purposes of any provision of this Agreement providing for the payment of any amounts or benefits upon or following a termination of employment unless such termination is also a “separation from service” (within the meaning of Section 409A of the Code).

c. It is intended that this Agreement comply with the provisions of Section 409A of the Code so as to not subject the Participant to the payment of additional interest and taxes under Section 409A of the Code, and in furtherance of this intent, this Agreement shall be interpreted, operated and administered in a manner consistent with these intentions.

[Signature Page Follows]

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IN WITNESS WHEREOF, the Company has caused this Performance Award Agreement to be executed by its duly authorized officer, and the Participant, to evidence his or her consent and approval of all the terms hereof, has duly executed this Performance Award Agreement, as of the date first written above.

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