LoglineWhen the USS Enterprise investigates an attack on a colony at the edge of Federation space, Captain Pike and his crew face the return of a formidable enemy.
Chekov was on the Enterprise during s1. Continuity with TWOK requires it. Plus some of the star dates for s2 episodes that starred Chekov where set before the star date for Space Seed.
But yes at this point we are ~6 years before TOS so Chekov would be in his late teens.