The USS Yorktown was a Federation starship that was in service during the latter half of the 23rd century.
In 2268, the Yorktown was scheduled to deliver vaccines bound for the colony on Theta VII after a rendezvous with the USS Enterprise. (TOS: "Obsession")
In 2286, the Yorktown was under the command of Captain Joel Randolph. While deployed near the Sol system, the Yorktown was one of the many vessels disabled by the Whale probe near Earth.
In Randolph's distress call to Starfleet Command, he noted that the ship had lost all power and that all non-essential crew were given hiber-sedatives to slow down consumption of life support reserves. Meanwhile, the chief engineer attempted to deploy a makeshift solar sail so as to focus and absorb radiation from a nearby sun they were orbiting, with the hopes of generating power to keep the crew alive. (Star Trek IV: The Voyage Home)
In 2293, Tuvok's father was a Starfleet officer serving aboard the Yorktown. (VOY: "Flashback")
Yorktown personnel
Background
According to an article by Greg Jein in a 1970s fanzine regarding starship registries, he assigned the number NCC-1717 to the name Yorktown. This registry has been further propagated by being included in the writings of Michael Okuda, such as the Star Trek Encyclopedia, which also references the Yorktown as a Template:ShipClass starship.
The Yorktown was listed as a Constitution-class starship, with the registry NCC-1704, in Franz Joseph's Star Fleet Technical Manual. However, much of the information in that manual that wasn't used on screen in some form is considered non-canon.
The USS Yorktown was the name of the central starship in Gene Roddenberry's first Star Trek proposal to NBC in 1964. The ship was named after the USS Yorktown, a World War II American aircraft carrier, which in turn was named after the last major battle of the American Revolution, won in 1781 by a combined Franco-American army commanded by Gen. George Washington.
Gene Roddenberry, in a nod to his original name choice from 1964, suggested that the Yorktown was renamed USS Enterprise-A at the end of Star Trek IV, explaining why the latter ship seemed to be launched so quickly at the end of the movie. The Next Generation fourth season writer's technical manual also indicates this to be the case. However, there is no primary evidence to confirm this theory. If the NCC-1701-A was refit from a ship from the TOS era, that would mean that the Yorktown was renamed after over 20 years of service – a seemingly disrespectful violation of starship naming parlance. However, if the Yorktown Roddenberry spoke of was a brand new ship, then why would it have been decommissioned only seven years later in Star Trek VI: The Undiscovered Country? Scrapping a relatively new cruiser seems like a waste.
A third possibility is that the Yorktown Roddenberry meant was neither aged nor young: Presuming the TOS Yorktown long-since retired, it could've been replaced by a Constitution ship of the movie-era several years hence. This would mean considering the TOS-era ship and the 2280s ship as two separate incarnations.
A fourth, closely related, possibility is that the original Yorktown, after being refit in the early 2270s, was retired in the early 2280s along with most of the other refit Constitution-class ships in preparation for the launch of the new Excelsior and Constellation classes. The refit Yorktown would have been replaced by a new (Miranda- or Constellation-class ?) ship. When two operational vessels (first the Reliant, then the Grissom) were lost in 2285, Starfleet would have needed a short-term replacement until new vessels could be constructed. The original Yorktown would have been pulled out of mothballs to fill this short-term role, but since there was already a new Yorktown in service (seen in Star Trek IV: The Voyage Home), a new name would have been needed for the original vessel. Because the original Enterprise had been destroyed over Genesis, and its Excelsior-class replacement (NCC-20XX) was still seven years away, the original Yorktown was renamed Enterprise NCC-1701A. In spacedock, the then-building Excelsior-class Enterprise would have been renumbered NCC-1701B. This possibility allows the original Yorktown to be renamed without any disrespect to the crew that suffered the probe-induced power loss in Star Trek IV: The Voyage Home (i.e., why would admiralty take a starship away from the captain who just saved his entire crew after its encounter with the whale probe, and give it to an officer who'd been demoted for insubordination?). It also allows that the Enterprise-A would have been a 40 year old vessel pressed back into service on a temporary basis, and that Tuvok's father would have served aboard the newer Yorktown.
A fifth possibility is that one of the writers totally missed something along the way, and, in trying to account for fan fiction in his drunken state, screwed up.
If the Yorktown was indeed renamed as the Enterprise-A, then Tuvok's father's ship must be a different Yorktown. However, if you disregard Roddenberry's behind-the-scenes commentary, there is no on-screen evidence that contradicts the three 23rd century mentions of the Yorktown name all being the same vessel.
The FASA sourcebook Star Trek: The Next Generation Officer's Manual lists a USS Yorktown (NCC-2033) of this era which belonged to the Template:ShipClass; the book, however, is not considered canon.
In the Star Trek: The Next Generation novel Crossover, the Yorktown is revealed to have become a museum exhibit on a starbase, but its bridge has been replaced with the original bridge of the first Enterprise. In the story in question, Captain Montgomery Scott steals the Yorktown to rescue Spock, recently captured by the Romulans, and fits it with an ancient Romulan cloaking device (the one acquired in "The Enterprise Incident"). The mission proves successful, but aid is still required from the USS Enterprise-D for Spock, Scotty and the Unification movement to escape.