Tex. Local Government Code § 81.021

(a) A commissioners court that orders a change in the boundaries of commissioner or justice precincts may specify in its order an effective date of the change that is not later than January 1 following the next general election. An election for precinct office occurring after the date that the order is issued but before the effective date of the change in boundaries shall be held in the precincts as they will exist on that effective date. A person who has resided in the area included in a new precinct for the period required for eligibility to hold office is not made ineligible on the ground that the precinct has not existed for that period.

(b) The term of office of a commissioner, justice of the peace, or constable who holds office at the time a change in precinct boundaries becomes effective is not affected by the change, regardless of whether the change places the officer's residence outside the precinct for which the officer was elected. The officer is entitled to serve for the remainder of the term to which the officer was elected.