U.S.S. Enterprise A
from "Star Trek IV: The Voyage Home" (1986)
About the Design
Seen only briefly at the close of "Star Trek IV: The Voyage Home," the Enterprise-A was Starfleet's "gift" to the courageous ex-Admiral -- now "Captain" -- James T. Kirk following the loss of the original refit Enterprise in "Star Trek III: The Search for Spock" and his subsequent rescue of Earth from the deadly "whale probe." Although the origins of the "A" were never disclosed in the film itself, Star Trek lore now has it that the ship was the former U.S.S. Yorktown, subsequently renamed in honor of the famous Big-E. This backstory was no doubt a nod to the origins of the original TV Enterprise, which in its earliest incarnations was, in fact, named U.S.S. Yorktown before someone put it in Gene Roddenberry's head to christen her Enterprise.
("Yorktown" would return as the name of the Federation space station featured in 2016's "Star Trek Beyond".)
About the Kit
AMT -- later AMT/Ertl -- produced new editions of the "refit" Enterprise to accompany each release of the "Star Trek" films from "Star Trek - The Motion Picture" in 1979 to "Star Trek VI - The Undiscovered Country" in 1991. The first kit is now know as the "Smoothie" because of its smooth, undetailed hull; later versions had panel lines engraved directly into the plastic. The original kit was also featured absolutely horrible rub-on decals instead of conventional waterslide, and rainbow-colored metallic stickers to cover the nacelle vents.
This particular model is of the "Enterprise-A," which appeared in "Star Trek IV - The Voyage Home" (1986), "Star Trek V - The Final Frontier" (1989) and "Star Trek VI - The Undiscovered Country" (1991). It is virtually identical to the original "refit" except for the "A" in its registration number. (Hell, it was the same miniature!)
The model itself is the "Star Trek V" version, which came with an itsy-bitsy shuttlecraft (not shown).