No, this is a new Star Trek Series starring Anson Mount (Hell on Wheels) as Captain Christopher Pike. The original Captain of the Enterprise and Rebecca Romijn as Number One the original First Officer originally portrayed by Jeffrey Hunter and Majel Barret both characters were never originally seen on screen as they were in the unaired 1965 Pilot titled "The Cage" and then later as Parts 1 & 2 of the Season 1 episodes titled "The Menagerie" in 1966.
I'm not sure on the timeline details.
I think all the new Paramount Star Trek series are now a mixture of both the Original Roddenberry Series & the 2009 Film timeline.
Mount, Romijn and Ethan Peck who portrays Spock were originally in the Star Trek: Discovery Season 2. This series is a prequel to their Discovery appearances.