Texas Local Government Code - LOC GOV'T § 26.043. Filling Vacancy in Elective Office in Municipality with Population of 384,000 or More

(a) If a vacancy occurs in an elective office of a municipality with a population of 384,000 or more and if the charter of the municipality does not provide for the filling of the vacancy, the governing body of the municipality, by majority vote, shall appoint an individual to fill the vacated office for the unexpired term. Pending that appointment, the governing body may appoint a person on a temporary basis to serve for a period not to exceed 60 days.

(b) A person appointed under Subsection (a) must possess the qualifications required of the elected official.

(c) If the municipality holds an election to vote on proposed amendments to its charter, it shall at that time submit a proposed charter amendment to provide a method for filling vacancies in elective offices.