A Constitution-class starship contemporary with Kirk's Enterprise, which took part in the M-5 war games and is mentioned in several original and animated series episodes.
The Potemkin is one of the Enterprise's sister ships in the 2260s. In The Ultimate Computer it is one of four starships, with the Lexington, Excalibur and Hood, that Commodore Wesley leads in war games against the Enterprise while the M-5 computer is in control. M-5 treats the drill as real and attacks, crippling the Excalibur, before Kirk talks it into shutting down.
The ship is named again in Turnabout Intruder, where the Enterprise is due to meet it at Beta Aurigae, an appointment Janice Lester, in Kirk's body, chooses to ignore. In the animated episode The Pirates of Orion the Potemkin passes a supply of the drug strobolin to the freighter Huron for delivery to the Enterprise when Spock contracts choriocytosis.