Texas Occupations Code - OCC § 552.005. Terms;  Vacancy

(a) Members of the board are appointed for staggered six-year terms, with either three or four members' terms, as applicable, expiring every other year at midnight on the last day of the state fiscal year in the last year of the member's term.

(b) If a vacancy occurs during a member's term, the governor shall appoint a replacement to fill the unexpired term.

(c) A board member may not serve more than two consecutive full terms.  The completion of the unexpired portion of a full term is not service for a full term for purposes of this subsection.

(d) A person appointed by the governor to a full term before the expiration of the term of the member being succeeded becomes a member of the board on the first day of the next state fiscal year following the appointment.

(e) A person appointed to an unexpired portion of a full term becomes a member of the board on the day after the date of appointment.