Texas Health and Safety Code - HEALTH & SAFETY § 101A.103. Terms;  Vacancy

(a) Oversight committee members appointed by the governor, lieutenant governor, and speaker of the house serve at the pleasure of the appointing authority for staggered six-year terms, with the terms of three members expiring on January 31 of each odd-numbered year.

(b) If a vacancy occurs on the oversight committee, the appropriate appointing authority shall appoint a successor in the same manner as the original appointment to serve for the remainder of the unexpired term.  The appropriate appointing authority shall appoint the successor not later than the 30th day after the date the vacancy occurs.