It has been stated in a number offical trek publications that the Enterprise-A was the recently decommisioned Yorktown.
When the original Enterprise was to be decomissioned a new Excelsior class ship was to take it place. We all know what Scotty had done to the engine on that ship and Starfleet figured out that transwarp drive was not going to work.
So all ships that were in under construction and including the Excelsior had their engine plants replaced with exsisting warp engines. Which took time and computer simulations to design a warp core to fit the ship design specifications.
As a result Kirk was assigned the Yorktown and it was re-commsioned as the Enterprise A. A thank you for saving Earth from the Federation Councle.
That is why in Generations you get to see the Enterprise B and after the evetns of Star Trek 6 the Enterprise A was a mess and Starfleet decided to not rebuild it but to replace it with Modifide Excelsior class.
By that time the Enterprise A was the only remaining Constitution class ship still in service was close to fourty years old. As a result Starfleet felt it was better to scrap it then repair it.
That is why the bulk of Starfleet between the kirk years and Picard are made up of Excelsior class ships.
Also I think Kirk continued to service as the Captian of the Ent. A along with his crew between STV and ST6 and it is possible that while they were on shore leave (thirty days leave) Spoke was with this father working on a peace treaty with the Klingons.
Now we have no menthion in the movie what the crew was doing before events of STVI to assume they were on stand down status or not except when Kirk says to spock that and most of his command staff was planning to retire before they were picked for the mission to excort the Klingon Chancaler to earth.