Starbase 31 was a Starfleet facility in operation in the late 23rd century.
In 2264, the USS Enterprise travelled to Starbase 31 to take Admiral Ellen Mangione aboard, for a mission into the Klingon Neutral Zone. (TOS - My Brother's Keeper novel: Enterprise)
Several years later, the Enterprise picked up Ambassador Gett'Ipher at Starbase 31 to transport him to Algol Prime. (TOS short story: "Make-Believe")