Star Trek Expanded Universe

USS John F. Kennedy was an Constitution-class heavy cruiser in active Starfleet service during at least the 2270s.

She was commanded by Commodore Katha'sat. (Star Trek: The Original Series novel: The Wounded Sky)

Hobbyist's Guide to the UFP Starfleet[]

In this continuity, this ship was an Achernar-subclass heavy cruiser. She had been exported to the Xindi for a time in the 2260s, named XXS Naxu Thain, then reacquired by Starfleet and renamed John F. Kennedy in 2269. (Hobbyist's Guide to the UFP Starfleet, Part 1a))