Texas Health and Safety Code - HEALTH & SAFETY § 103.008. Vacancy

(a) The office of a member appointed by an agency becomes vacant when the person terminates employment with the agency or when the agency elects to replace the person as provided by Section 103.005.

(b) If the office of a member who is an agency representative becomes vacant, the commissioner or executive commissioner, as appropriate, of that agency shall appoint an agency representative to serve for the remainder of that member's term.