Starbase 10 was a Federation starbase that was administered by Starfleet. The base was located in the Alpha Quadrant, near Deneva. A direct course from Gamma Hydra to this base would pass through the Romulan Neutral Zone. This star fell into the administrative area of the base.
In 2267, the USS Enterprise traveled to this base following its mission to Deneva. Later that year, Commodore Stocker was assigned command of the base and was transported there by the Enterprise. (TOS: "Operation -- Annihilate!", "The Deadly Years"; VOY: "Tinker Tenor Doctor Spy")
In 2399, the location of Starbase 10 was labeled in a Federation star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters. This base was located in or near to Federation space. (PIC: "Maps and Legends")
This base was also mentioned in gaming reference books (The Triangle Campaign, Starfleet Operations Manual), novels (Pocket TNG: Red Sector), and comics (Gold Key TOS: "Sceptre of the Sun" and Peter Pan Records: "The Robot Masters").