Starbase 24 was a Federation starbase administered by Starfleet. This base was located close to the Federation-Klingon border in the Beta Quadrant. It was located near Gamma Hromi, Ramatis, and the Federation border with the Klingon Empire.
In 2256, this starbase's location was labeled on the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery. (DIS: "Magic to Make the Sanest Man Go Mad")
In 2257, during the Federation-Klingon War, this starbase was occupied by the Klingons. (DIS: "The War Without, The War Within")
Later that year, its location was labeled on the star chart showing the trajectory of Lieutenant Spock's shuttle. (DIS: "An Obol for Charon")
In 2293, the starships USS Constellation and USS John Muir were at this station. The Constellation was there for certification tests and the John Muir was there for a system upgrade. The starbase was named on a Starship Mission Assignments chart on the USS Enterprise-A bridge.
Later that year, in the "Operation Retrieve" command briefing, Starbase 24 was depicted as being in the theater of operations. (Star Trek VI: The Undiscovered Country)
In 2346, the USS Intrepid transported Worf's nursemaid, Kahlest, to Starbase 24 where she could be treated for her injuries at the base's biomedical facility. The starbase, due to its proximity to Khitomer, had the best records of the Khitomer Massacre in 2366. (TNG: "Sins of the Father", "Redemption")
In 2399, the starbase's location was labeled on a star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters. (PIC: "Maps and Legends")
Kahlest's medical file seen in "Sins of the Father" stated she was transported to Starbase 23 and not Starbase 24, as was stated in the dialogue.