Tex. Health & Safety Code § 102.103 – Terms; Vacancy

(a) Oversight committee members appointed by the governor, lieutenant governor, and speaker of the house serve at the pleasure of the appointing office for staggered six-year terms, with the terms of three members expiring on January 31 of each odd-numbered year.
(b) Not later than the 30th day after the date an oversight committee member's term expires, the appropriate appointing authority shall appoint a replacement.
(c) 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.
Acts 2007, 80th Leg., R.S., Ch. 266 (H.B. 14), Sec. 4., eff. November 6, 2007.
Acts 2009, 81st Leg., R.S., Ch. 368 (H.B. 1358), Sec. 3, eff. June 19, 2009.
Acts 2013, 83rd Leg., R.S., Ch. 1150 (S.B. 149), Sec. 12, eff. June 14, 2013.