The Spock of this timeline thought that, logically, he should resign his commission in Starfleet to help restore Vulcan civilization, but his "older self" urged him to remain, so as not to be denied the potential accomplishments made with his friendships with the crew of the USS Enterprise, specifically James T. Kirk. (Star Trek)
Within a year, New Vulcan had become the capital of the Confederacy of Surak. In 2259, the Enterprise contacted this planet, where Spock Prime revealed the true nature of Khan Noonien Singh to the crew. (Star Trek Into Darkness)
In 2263, Spock Prime passed away on New Vulcan. The younger Spock again considered resigning his commission and returning to New Vulcan to help rebuild the Vulcan race, but after defeating Krall at Starbase Yorktown, decided to remain in Starfleet and accompanied the others when the USS Enterprise-A was launched. (Star Trek Beyond)
New Vulcan is one of the settings of the 2013 Star Trek video game, set between the events of Star Trek and Star Trek Into Darkness. In the game, it is invaded by the Gorn, leading to the destruction of infrastructure and loss of life.
According to the "Legacy of Spock" arc of the Star Trek: Ongoing series, more than 27 million Vulcans survived the destruction of Vulcan and planned on relocating to Ceti Alpha V. It wasn't until Ambassador Spock initiated a mind meld with the Vulcan elders that the Vulcans learned of Ceti Alpha V's eventual fate, and decided to settle on the second planet of the Simon-316 system instead. Spock Prime has a monument made there in his likeness that is still standing 3,000 years later.