|Owner:||United Federation of Planets|
The Endeavour was on a deep space exploration mission near Klingon territory in 2293. This ship, along with the USS Ahwahnee and the USS Emden, was selected as additional support for Operation Retrieve, which would have rescued Captain James Kirk and Doctor Leonard McCoy from Rura Penthe. (Star Trek VI: The Undiscovered Country)
This starship and it's registry number were not referenced in dialog. This vessel appeared in the plans for Operation Retrieve presented by Colonel West. Save for the USS Excelsior, the Eagle and five other starships were graphically represented by the silhouette of a movie era refit-Constitution-class vessel. According to the starship listing included on page four of the Operation Retrieve mission plans, which however was not seen in the extended cut of the movie, the Endeavour was commanded by D. Wise, and the ship was located in Sector 22849. The ship's captain was named after the sixth movie's first assistant director Douglas E. Wise. 
The Endeavour was a starship name considered by the producers at the start of second season of Star Trek: The Original Series for inclusion in the definitive fourteen ship list belonging to the Constitution-class, at the time still referred to as "Starship-class" by them. It was mentioned in the first two proposals, but ultimately did not make the cut. (The Making of Star Trek, pp. 164-165) The name was considered due to the fact that page 27 of the first draft treatment of the script, dated May 15, 1967 for the second season episode "Amok Time", contained a line having Captain Kirk state,
The reference though, was dropped from the episode as aired. 
Franz Joseph's reference book Star Trek Star Fleet Technical Manual gave the Endeavour the registry NCC-1716 and Greg Jein's influential "The Case of Jonathan Doe Starship" article gave it the registry NCC-1718. When creating the charts for Star Trek VI: The Undiscovered Country, Michael Okuda chose to invent a new number for the ship.  Okuda has since then propagated the number throughout his subsequent reference book writings. Early editions Star Trek Encyclopedia also listed the ship as a Constitution-class vessel, whereas the last edition dropped the entry for the 23rd century vessel altogether.
The Endeavour was presumably named for the HMS Endeavour, specifically, the HM Bark Endeavour commanded by Lieutenant James Cook in his voyage of exploration in the Pacific from 1768–1771, and the NASA space shuttle Endeavour.
The Pocket TOS Errand of Vengeance novel Killing Blow features a USS Endeavor engaging Klingon forces at the Battle of Donatu V in 2245. This Endeavor was referred to as an Icarus-class (β) starship in Errand of Fury: Seeds of Rage.