If for any reason a vacancy shall occur in the board, the chair shall prepare a notice to the governor asking for the appointment of a new member to fill the unexpired term. If the vacancy shall occur in offices of vice chair, secretary, or treasurer of the board, the board shall elect a new officer to serve for the remainder of the unexpired term from its own membership at the first regular or special meeting following the vacancy.
22 Tex. Admin. Code § 131.13