I'd like to at least think he's the same Pavel Chekov of the TOS universe, so I guess if I had to come up with an in-universe explanation for the four year difference in age it would be a transporter accident.
Wouldn't it be much simpler to assume Chekov simply misstated his age in "Who Mourns for Adonais," that for some reason he said 22 when he was 26? Maybe he wasn't using Earth years. Maybe he had some reason to pretend to be younger than he was.
The simplest solution of all would be just to ignore the "Twenty-two, sir" line in "Adonais" and assume he said 26 instead, or maybe 25 depending on where in the year it fell. Heck, there are plenty of other numbers and minor details in Trek that we simply have to ignore, like "James R. Kirk" and the timing discrepancies I mentioned in several above posts.
Or ignore the the 17 and just assume Chekov got into the academy early. They can't make everyone enroll at the same age. If there was an Ocampa wanting to join they'd be long dead before they could enroll. So Chekov's 13 instead of 17. Worked for Doogie Howser.