Texas Local Government Code - LOC GOV'T § 22.010. Filling Vacancy on Governing Body or in Other Municipal Office

(a) If for any reason a single vacancy exists on the governing body of the municipality, a majority of the remaining members who are present and voting, excluding the mayor, may fill the vacancy by appointment unless an election to fill the vacancy is required by Section 11, Article XI, Texas Constitution. The mayor may vote on the appointment only if there is a tie.

(a-1) A person serving as a member of the governing body is not, because of that service, ineligible to be appointed to fill a vacancy in the office of mayor of the municipality, but the person may not vote on the person's own appointment.

(b) The person appointed to fill the vacancy serves until the next regular municipal election.

(c) In lieu of appointing a person to fill a vacancy on the governing body, a special election may be ordered to elect a person to fill the vacancy.

(d) If two or more vacancies on the governing body exist at the same time, a special election shall be ordered to fill the vacancies.

(d-1) A member of the governing body is ineligible to vote to fill a vacancy on the governing body by special election after resigning from the governing body.

(e) If a vacancy exists in any other municipal office, the mayor or acting mayor shall appoint a person to fill the vacancy, subject to confirmation by the governing body.