Tex. Elec. Code § 232.047
(a) If a candidate who is a nominee of a political organization in a new election ordered by a court in an election contest involving a city office for which partisan nominations are permitted dies or is declared ineligible before the date on which the district court sets the date for the new election, the candidate may be replaced only by a replacement nominee named in the manner prescribed by:
Acts 1985, 69th Leg., ch. 211, Sec. 1, eff. Jan. 1, 1986.