New Vulcan was a colony established by the Vulcan race following the destruction of Vulcan at the hands of the Romulan Nero in an alternate reality. (TOS movie, novelization & comic adaptation: Star Trek; TOS video game: Star Trek)
According to a status display in the office of Admiral Alexander Marcus, the new name of the Vulcan government - with New Vulcan as its capital - is the Confederacy of Surak. In 2259, following the attack on Helios-1, New Vulcan came under attack by the Gorn who kidnapped Surok in order to get the Helios device. After the USS Enterprise pushed the Gorn back, Surok's daughter T'Mar was returned to New Vulcan.
Later that year, Spock spoke with his counterpart, Spock, via a subspace message. Young Spock asked his older self if he had ever encountered Khan in his timeline and how Khan could be defeated. Older Spock replied that Khan was the most dangerous enemy they had ever encountered, and that Khan was eventually defeated "at great cost." (TOS video game: Star Trek; TOS movie: Star Trek Into Darkness)
Ambassador Spock had died in January of 2263. Following the destruction of the USS Enterprise at Altamid in the same year , Spock and Nyota Uhura took a sabbatical to Sarek's home. There, Spock assisted the Vulcan High Council in establishing New Vulcan's Science Academy. However, Spock and Uhura asked the High council to borrow a D'Kyr-class cruiser to assist the USS Endeavour in dealing with the Borg threat. (TOS - Boldly Go comics: "Issue 1", "Issue 2")
Vulcan civilization would thrive on the new world over the next 3,000 years. By approximately 5259, a statue of Spock was built on the planet. While many of the surrounding monuments were larger than life, the monument of Spock was life size. This was at Spock's request, as he felt a larger than life monument would not be logical. (TOS - Legacy of Spock comic: "Part 4")