New Vulcan was a colony established by the Vulcan race following the destruction of Vulcan at the hands of the Romulan Nero in the Kelvin timeline. (TOS movie, novelization & comic adaptation: Star Trek; TOS video game: Star Trek)
The colony was founded on the second planet of the Simon-316 star system, following its selection by Spock Prime in early 2258, and after the previous proposed colony-site at Ceti Alpha V was deemed too risky to settle, due to its future fate being made known to the Vulcan High Council by the elder Spock via mind-meld. (TOS - Legacy of Spock comic: "Part 4")
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 – was 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)
In 2260, Enterprise returned to New Vulcan to resolve Spock's pon farr. Due to the geophysical differences between New Vulcan and the late planet Vulcan, Spock's blood fever intensified and the joined a lost tribe of Vulcans, the Sasaud. The Enterprise crew developed a cure, and recovered Spock with the other Sasaud. T'Pring was grateful for restoring the lost Vulcans to sanity. (TOS - After Darkness comic: "Part 2")
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")