Texas constitution
Article 11: municipal corporations
Section 11

(c) Any vacancy or vacancies occurring on such governing body shall not be filled by appointment but must be filled by majority vote of the qualified voters at a special election called for such purpose within one hundred and twenty (120) days after such vacancy or vacancies occur except that the municipality may provide by charter or charter amendment the procedure for filling a vacancy occurring on its governing body for an unexpired term of 12 months or less.