Starbase 24 was a Starfleet starbase located near Khitomer and was the proposed jumping off point for Operation Retrieve in 2293.
The USS John Muir docked at Starbase 24 for an upgrade in 2293. (Star Trek VI: The Undiscovered Country)
In 2346, Worf's nursemaid, Kahlest, was taken to the biomedical facility at Starbase 24 for treatment following her rescue from Khitomer by the USS Intrepid. The starbase, due to its proximity to Khitomer, had the best records of the Khitomer Massacre in 2366. (TNG: "Sins of the Father", "Redemption")
Kahlest's medical file seen in "Sins of the Father" mistakenly reads Starbase 23 and not
Starbase 24, as was stated in the dialog.