Tex. R. Disc. P. 2.03
All persons serving on a Committee at the time these rules become effective shall continue to serve for their then unexpired terms, subject to resignation or removal as herein provided. Nominations to Committees shall be made annually at the spring meeting of the Board; all appointments shall be made by the President no later than June 1 of each year, provided, however, that if a vacancy on a Committee arises after June 1, the Director(s) shall nominate and the President shall appoint an eligible person to serve for the remaining period of the unexpired term. If any Director fails or refuses to make nominations in a timely manner, or the President fails or refuses to make appointments in a timely manner, the existing members of the Committees shall continue to hold office until the nominations and appointments are made and the successor member is qualified. One-third of each new Committee will be appointed for initial terms of one year, one-third for an initial term of two years, and one-third for an initial term of three years. Thereafter, all terms will be for a period of three years, except for appointments to fill unexpired terms, which will be for the remaining period of the unexpired term. Any member of a Committee who has served two consecutive terms, whether full or partial terms, is not eligible for reappointment until at least three years have passed since his or her last prior service. No member may serve as chair for more than two consecutive terms of one year each. All members are eligible for election to the position of chair.
Tex. R. Disc. P. 2.03