This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
In 2364, the helmsman of the USS Enterprise-D, Geordi La Forge, suggested the USS Enterprise-D could deliver their late-20th century passengers at this starbase. It was five days away, at warp 8, from the position of the Enterprise-D at the edge of the Romulan Neutral Zone in Sector 30. According to La Forge, it would reduce their travel time back to Earth by months. Additionally, Captain Picard thought the extra time would allow them to better acclimate to the 24th century. (TNG: "The Neutral Zone")
In 2399, the location of Starbase 39-Sierra was labeled in a star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters. This base was in or near to space claimed by the Romulan Free State. (PIC: "Maps and Legends")
In 3190, the location of this starbase, identified as Starbase 39, was labeled on a star chart used by Commander Paul Stamets for tracking the movement of the Dark Matter Anomaly through the galaxy. (DIS: "The Examples")
This starbase was only mentioned in dialogue.
According to Star Trek: Star Charts (p. 66, "United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Starbase 39-Sierra was located in the Kaleb sector.
The Star Trek: Typhon Pact novel Rough Beasts of Empire also mentions the starbase, placing it in the Sierra system (β) in the Sierra sector (β). Starbase 39-Sierra was prominently featured in the game Star Trek Online, in which it served as a hub for Federation missions along the Romulan Neutral Zone.