In the real world, the original plan was to move everyone on the Excelsior and call it a day, but it soon became clear that the fans would not accept that and that even a new excelsior-class enterprise wouldn’t be welcome. Gene Roddenberry himself hated the idea and let people know of the studio’s plans, starting petitions against it.
Since the new enterprise appeared in Star Trek IV only for a few seconds and there was no guarantee of a fifth movie, designing and building an expensive new model was deemed unnecessary, especially as the refit-enterprise was much loved and a perfectly good model of that was available, so the studios decided to just change the lettering and go with it, even if it ended up condemning the VFX crew of the next two movies to the duress that that model involved: it was huge, heavy, and very hard to work with, it’s a beautiful model but everyone hated working with it.
Something similar happens with the reboot enterprise-a, which also got a minor redesign that helps differentiating it from her predecessor, something useful to sell toys, but doing that back in the 80s would have been expensive and was never really considered.
In universe, we never know if the E-A is a new ship of an old design or an old ship with a new name, but it’s quite obvious that christening her with Kirk in command was a big publicity stunt while also being a way of getting rid of Kirk himself and his command staff.
In Star Trek II/III we see Spock being captain of the Enterprise, Scotty being put in charge of a very important project, sulu on the verge of getting his own ship, Chekov being first officer on the Reliant and Uhura being able to request any post she wanted, by Star Trek V their careers were back to the positions they had some 15 years earlier, with no possibility of advancement, on a figurehead ship that’s sent mediating a dispute on an unimportant planet, seven years later, with most of them on the brink of retirement, very little has changed, only Sulu having managed to get his own command.
After the battle with Chang it doesn’t seem like the ship is about to be decommissioned, so it’s possible it served under another senior staff for a few more years. I find it also very believable that it was deemed too damaged to be worth repairing and mothballed (or sold off to an independent planet on the Klingon/Romulan border...nah, that’s not canon), with a few years passing before the launch of the B.