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The USS Intrepid (NCC-1631) was a Federation Constitution-class heavy cruiser that was in service with Starfleet in the mid-23rd century. This ship was crewed almost entirely by Vulcans. (TOS: "The Immunity Syndrome")
In 2267, the Intrepid was undergoing repairs in maintenance section 18 at Starbase 11. The base commander, Commodore Stone, rescheduled the Intrepid's repairs, upon giving the USS Enterprise "Priority one" status on stardate 2947.3, after being damaged in an ion storm. (TOS: "Court Martial")
In 2268, the Intrepid worked in conjunction with Starbase 6, in conducting a mission to investigate the loss of contact with star system Gamma 7A in Sector 39J. While traversing that sector of space, the Intrepid encountered an unknown dark zone which was, unbeknownst at the time, slowly killing the ship's crew.
On stardate 4307.1, Starbase 6 lost contact with the Intrepid. A rescue priority was issued to the Enterprise to investigate the loss of the Intrepid in an unknown dark zone. En route, Commander Spock telepathically sensed the crew of four hundred Vulcans die.
On stardate 4309.2, the Enterprise established that the thing which destroyed the Intrepid and the Gamma 7A system was an incredibly huge but simple cellular being whose energies were totally destructive to all known life. The crew of the Enterprise destroyed the form, which was determined to be nourishing itself for reproduction. (TOS: "The Immunity Syndrome")
The Star Trek Encyclopedia described this vessel as a Constitution-class starship, with a registry of NCC-1631 (diagram) or NCC-1831 (list). The registry NCC-1831 was seen in the chart in TOS: "Court Martial". Unfortunately, the chart doesn't provide names to the registries. Greg Jein also originally used 1631. See the Constitution-class article for the full explanation. The Star Fleet Technical Manual assigned NCC-1708 to the vessel. According to the Manual, this ship's successor was to be called USS Intrepid II NCC-1730 and to be Constitution-class.
Due to the crew count of 430 that the producers of TOS mentioned in the dialog for "The Immunity Syndrome," it was a likely assumption they intended this vessel to be Constitution-class. This was confirmed by the appearance of the ship in TOS: "Court Martial" remastered, where the USS Intrepid was seen in orbit of Starbase 11 with the registry NCC-1631.
Like the Intrepid, the USS Hera and USS T'Kumbra also had a predominantly Vulcan crews. According the Star Trek Concordance by Bjo Trimble, the captain of the Intrepid was Satak. This reference, like that of the similarly-referenced IKS Devisor, may have been acquired from an early draft of the script. The Worlds of the Federation by Shane Johnson refers to a captain of this vessel being named Spiak.
The Star Trek: Phase II episode "Deadlock" was set to open with the Enterprise receiving a distress call (which later turned out to be fake) from the Intrepid, which by that point had been presumed destroyed for nearly five years.
The Intrepid may have been named after any number of Royal Navy (HMS Intrepid) or US Navy (USS Intrepid) vessels which had borne the name. The lunar module of NASA's Apollo 12 was also known as Intrepid. In all cases, the name signified a willingness to go in harm's way to accomplish a mission of great importance.
Several novels mentioned the second Constitution-class Intrepid, such as My Enemy, My Ally and Prime Directive (Pocket TOS). Prime Directive has the under-construction Intrepid's nacelles diverted to be attached as replacements on the Enterprise, and My Enemy, My Ally described Intrepid, under Captain Suvuk, as being slightly more advanced than the as yet un-refit Enterprise of that era. My Enemy, My Ally refered to Intrepid, named so for the ship destroyed by the giant amoeba, as NCC-1631 a number previously used in Greg Jein's original article and FASA manuals. FASA's Enterprise-class Intrepid had the registry NCC-1707 and would be in service around this time.