22 Tex. Admin. Code § 505.7
If for any reason a vacancy shall occur in the board, the chairman shall provide a notice to the governor and ask for the appointment of a new member to fill the unexpired term. If the vacancy shall occur in any of the offices of the board, the board shall elect from its own membership at the first regular or special meeting following the vacancy a new officer to serve for the balance of the unexpired term.
Source Note:The provisions of this §505.7 adopted to be effective December 24, 1979, 4 TexReg 4508.