Cinema Geekly wrote:
As a result Chekov may have entered into the academy at a different time, his interests may have changed in relation to his studies ultimately making a slightly different person from the PRIME Chekov.
But that doesn't explain the overt difference in the two Chekovs' ages. Chekov Prime explicitly gave his age as 22 in "Who Mourns for Adonais" (2267), and Abramsverse Chekov explicitly gave his age as 17 in the movie (2258), so there's a 4-year discrepancy.
Of course, there is one simpler explanation: Chekov Prime could've actually been 26 in "Adonais" but was claiming to be younger for some reason. But why would he pretend to be more inexperienced than he actually was? Normally you'd expect someone of that age and status to pretend to be older, not younger.
There's always the fallback idea that maybe he didn't mean 22 Earth
years, but given that he's pretty clearly from Russia, why would he use a different planet's calendar?