The USS El Nath (NCC-1835) was a Constitution-class Federation starship in service in the 23rd century. The ship was named for stars name El Nath (including Beta Tauri and Alpha Arietis). (ST reference book: Star Fleet Technical Manual).
In 2285 the El Nath was on patrol duty at Planet Gateway, the home of the Guardian of Forever. Contact with the ship was lost shortly after the destruction of the USS Constellation II in a separate area of space, and it was soon afterwards discovered that instances of time running either too quickly or too slowly was to blame for the Constellation II's demise.
The USS Enterprise under Admiral Kirk was sent to the Guardian to investigate the instances of unnatural time-flow and discover what had happened to the El Nath.
The ship was not on her assigned patrol route, but the Enterprise discovered that the apparent malfunctioning of the Guardian was caused by the return of the Guardian's creators.
While that situation was eventually resolved, no trace remained of the El Nath or her crew, and she was presumed destroyed by the events of that situation.