Or whatever ship this is that Captain April has was a starship Enterprise built after the NX-01 was retired, but before the NCC-1701 was built (in both universes). (The comic suggests this Enterprise was built sometime before the loss of USS Kelvin) Due to timeline changes, this Enterprise is lost or retired sometime before 2244 were a new Constitution-class starship takes the name with April taking command for is first tour of duty, while in the Kelvin Universe, with April goin AWOL and Marcus taking the ships, it is retained in service until the much larger Constitution-class ship (still named Enterprise) is completed in 2258. The decision to not retire the older ship in the 40s might be like in today's military, were politics can sometimes delay a replacement from being built for a very long time. The planned Connie design didn't work for what the Federation wanted, so another design was considered after some time. The larger ship took a bit more time to finish, leaving the old starship Enterprise long in the teeth by the time she was finally decommissioned by 2257.
This might have happened in the Prime Timeline, again with the Enterprise, but the replacement being the Excelsior-class and its delayed entry into the fleet and potential delay in construction of more of the class until the lead ship was proven. First leaving USS Enterprise in service possibly longer than intended, and then dragging out whatever the NCC-1701-A was originally for seven or so years of service while Excelsior was put through its paces, and an eventual replacement NCC-1701-B Enterprise could be built.