Texas Government Code - GOV'T § 25.2603. Vacancy

(a) A vacancy in the office of judge is filled by a joint appointment by the commissioners courts of the counties composing the court. An appointment must be approved by a vote of a majority of the total number of county judges and commissioners of the commissioners courts of the counties.

(b) An appointee holds office until the next general election and until the successor is elected and has qualified.

(c) This section applies to a vacancy existing on creation of the office of judge.