Starbase 313 was a Federation starbase administered by Starfleet.

The USS Enterprise-D stopped at Starbase 313 in 2367 to pick up scientific equipment for a Federation outpost in the Guernica system, as well as Doctor Leah Brahms, who came aboard to study Geordi La Forge's modifications to her original designs for the Enterprise-D's engines. (TNG: "Galaxy's Child")

This starbase was only mentioned in dialogue.