Actually, in this particular case it's vice versa: much as we and Kirk would like to think the ship is old, in actuality Honest Harry's Slightly Preowned Starships just screwed the old license plate to an all-new chassis, body, engine, upholstery and stereos. This is something of a plot point, even, with Kirk desperately wanting to relive the past and being blind to the fact that he cannot.
Kirk's career in general is a never-ending sacrifice, it seems: he always ends up behind the desk, then briefly getting command of a ship that doesn't meet his daydreaming expectations, then again behind the desk...
Timo Saloniemi