Texas Senate. The Texas Senate is the upper house of the Texas State Legislature. There are 31 members of the Senate, representing single-member districts across the U.S. state of Texas, with populations of approximately 806,000 per constituency, based on the 2010 U.S. Census. There are no term limits, and each term is four years long. Elections are held in even numbered years on the first Tuesday after the first Monday in November. In elections ending in years ending in 2, all seats are up for election. Half