Texas Business Organizations Code - BUS ORG § 22.212. Vacancy

(a) Unless otherwise provided by the certificate of formation or bylaws of the corporation, a vacancy in the board of directors of a corporation shall be filled by the affirmative vote of the majority of the remaining directors, regardless of whether that majority is less than a quorum.  A director elected to fill a vacancy is elected for the unexpired term of the member's predecessor in office.

(b) A vacancy in the board occurring because of an increase in the number of directors shall be filled by election at an annual meeting or at a special meeting of members called for that purpose.  If a corporation has no members or has no members with the right to vote on the vacancy, the vacancy shall be filled as provided by the certificate of formation or bylaws.