Except as otherwise provided by law, all members of advisory committees are appointed by and serve at the pleasure of the commission. If a member resigns, dies, becomes incapacitated, is removed by the commission, otherwise vacates his or her position, or becomes ineligible prior to the end of his or her term, the commission shall appoint a replacement who shall serve the remainder of the unexpired term.
30 Tex. Admin. Code § 5.7