Texas Election Code - ELEC § 201.053. Unexpired Term and Full Term Filled Simultaneously

(a) If, after the general election for an office for which a vacancy is filled by special election but before the succeeding full term begins, a vacancy occurs in both the unexpired portion of the current term and in the succeeding full term that was filled at the general election, the special election shall be ordered to fill only the full term.

(b) If any portion of the unexpired current term remains after the date the final canvass of the special election for the full term is completed, the person elected to the full term, if eligible to hold the unexpired current term, is considered to be elected to the remainder of the unexpired current term also and is entitled to qualify and assume office for the unexpired current term and the succeeding full term immediately on receiving a certificate of election. The certificate must recite that it is for both the unexpired current term and the full term.

(c) After qualifying for the unexpired current term, the person is not required to qualify again for the full term. If a bond is required, the amount of the bond for the unexpired current term and the full term is the same as for the full term.