If the board increases the number of directors under Section 3878.051, the board shall appoint eligible persons to fill the new director positions and shall provide for the staggering of terms of the new directors. On expiration of the term of a director appointed under this section, a succeeding director shall be appointed and qualified as provided by Subchapter D, Chapter 375, Local Government Code. The mayor and members of the governing body of the City of Houston shall appoint voting directors from persons recommended by the board. A person is appointed if a majority of the members of the governing body, including the mayor, vote to appoint that person.
Tex. Spec. Dist. Loc. Laws § 3878.052