Star Trek Expanded Universe

USS John F. Kennedy (NCC-1538) was an Einstein-class starship in active Starfleet service during at least the 2260s.

On stardate 3064.9, John F. Kennedy conveyed an officer from the USS Farragut to his next assignment. (Starship Farragut: "Dearly Departed")

The registry number of the JFK (Kelvin's is NCC-0514) suggests that there may have been more than one block of starships of this type and undetermined class.
Assuming that Starship Farragut's continuity and that of Diane Duane's pro novels are the same, this may have been upgraded to, or replaced by, a Constitution-class starship of the same name by the mid-2270s. (TOS novel: The Wounded Sky)