Tex. Civil Practice and Remedies Code § 172.145

(a) Except as agreed by the parties, an award of costs of an arbitration is at the discretion of the arbitration tribunal.

(b) In making an order for costs:

(1) the arbitration tribunal may include any expenses incurred in connection with the arbitration, including:

(A) the fees and expenses of the arbitrators and expert witnesses;

(B) legal fees and expenses; and

(C) administration fees of the institution supervising the arbitration; and

(2) the tribunal may specify:

(A) the party entitled to costs;

(B) the party required to pay costs;

(C) the amount of costs or method of determining that amount; and

(D) the manner in which the costs are to be paid.