It was mentioned in several places such as "Mr. Scott's guide to the Enterprise" that the 1701-A was originally the Yorktown (or Tiho?) and was renamed Enterprise to reward Kirk for saving the Federation once again.
This is from Memory Alpha:
According to Gene Roddenberry, the NCC-1701-A was not a newly-constructed ship, but instead was the renamed USS Yorktown, a nod to the name of the starship in his original pitch for Star Trek. This was based on the fact that it was difficult to believe that Starfleet would build a whole new ship in such a short time, and then decommission it a short while after, and the early retirement of the Enterprise-A could be justified if the ship had been in service for many years under another name.
Mr. Scott's Guide to the Enterprise, released shortly after Star Trek IV: The Voyage Home, cites the origin of NCC-1701-A as the USS Ti-Ho (NCC-1798), an Enterprise-class starship which was a test bed for transwarp technology alongside the USS Excelsior. The Ti-Ho was rechristened Enterprise after Kirk and his crew were exonerated.
I personally believe a combination of the two personally. The Enterprise-A was the Yorktown and it was used as a trials ship for technology destined for the Excelsior class ships.
Treknically speaking, according to Ships of the Star Fleet (Volume I), the Federation Reference Series, U.S.S. Enterprise Heavy Cruiser Evolution Blueprints, and other "serious" Treknical works of the 1980s...1701-A was a new-build starship originally to be named the U.S.S. Levant, basically an improved Enterprise class heavy cruiser with state-of-the-art new technology systems... Following ST IV, she was renamed Enterprise and thus, being the class ship, was named Enterprise (II) class--with provisions made for upgrading several existing Enterprise class heavy cruisers to these new specs...and there were new-builds, too, such as the U.S.S. America with cool rear-firing torpedo tubes mirroring the forward launchers in the interconnecting dorsal region...
The system breakdowns which we saw at the beginning of ST V were due to faulty peripheral interface adaptors to the main (brand-new) computer (Duotronic IV, never before tested on a heavy cruiser class ship--the ST-TMP Enterprise incidentally had Duotronic II). This ship did not have transwarp but a much more refined warp drive system permitting much faster velocities than the earlier incarnation (she also gained a linear shortcut to the galactic core via Cochrane's Factor/space density, explained in Star Trek Maps/Introduction to Navigation Manual--an old fan concept based upon E.T.A. specs mention in TOS episodes such as "That Which Survives")... Much of this is verified in the Starfleet Prototype manual, as well as the 1701-A Deck Plans blueprints from circa 1991... The early retirement of 1701-A sits with Sybok straining the ship's superstructure to the limit by taking her to the galactic center and back again at High warp speeds...and then Chang chucking a Klingon cannonball through her in ST VI...
At least Mr. Scott's Guide acknowledges the fact that Star Fleet can still build new starships. Non-Treknical fans have no sense of the Scope of the UFPs size and number of ships in service...exemplified in 2009's movie...
The junk about the U.S.S. Yorktown makes no sense for fans who actually saw ST IV: as we Saw the Yorktown in service. We're supposed to believe she was renamed and renumbered for demoted Kirk's sake? While it's true that Roddenberry liked the name Yorktown, the rest is pure conjecture, exaggeration, and is attributed to none other than Michael Okuda who also invented a wide range of NCC registries and ship classes for his encyclopedia, the year 2245 for the Enterprise's commissioning, and many other "facts" unsupported by a supposedly "canon" work that sticks to On Screen information.
How's that for Channeling?