According to the IDW
the events in the after darkness comics take place in 2259 one week after the very last scene of the movie and they're aboard the Enterprise refit not another ship.
I'm not sure anymore that there is an actual one year gap in the end.
here's a preview of the comic where you can see the ship:
I also have the novelization by Alan Dean Foster and the one year gap isn't mentioned either.
From Pine's delivery of the line, it's ambigous if "one year ago" means the movie's main events, or if he's referring to when he first officially took command of the Enterprise a year earlier (at the end of XI).
Personally, I prefer to assume the final scene is set a year after the main movie, it explains how the Enterprise was repaired, and Kirk and crew would likely need to stick around for a year anyway, for inquiries and tribunals which likely had to follow everything that went down. Really, a year is still not enough time for all that, but maybe beuracracy improves in the future?
Plus by placing the After Darkness comic in 2260, it's exactly seven years prior to Amok Time. That's kind of crucial to the plot of After Darkness.