Education Code §11.060

(a) If a vacancy occurs on the board of trustees of an independent school district, the remaining trustees may fill the vacancy by appointment until the next trustee election. (b) If the board is appointed by the governing body of a municipality, a trustee appointed by the governing body to fill a vacancy shall serve for the unexpired term. (c) Instead of filling a vacancy by appointment under Subsection (a) or (b), the board or municipal governing body may order a special election to fill the vacancy. A special election is conducted in the same manner as the district's general election except as provided by the Election Code. (d) If more than one year remains in the term of the position vacated, the vacancy shall be filled under this section not later than the 180th day after the date the vacancy occurs.