Kirk is in his mid-30s in season one, say 34 or 35. Checkov is a ensign, new to the
Enterprise but not necessarily just out of the Academy in season 2. (An officer in the U.S. Navy can remain an ensign for several years before winning promotion to Lieutenant, Junior Grade.) A typical midshipman is 22 when he graduates and joins the fleet as an ensign, so Checkov would hardly be "in diapers" when Kirk was at the Academy. The age difference between them is 10 years or less.
So it is not all that implausible that a 22 year old Kirk, in his last year at the Academy, might encounter a 14 or 15 year old Checkov. Nothing in the promo says that Chekov is
attending the Academy, it just says he's a character in the movie. Assuming that old Chekov and old Spock are reminiscing about Kirk it wouldn't be hard to work out a story where the teenaged Checkhov met, and perhaps even shared an adventure with, some starfleet cadets and was thus inspired to enroll in the Academy himself when the time came. (Nor would it be implausible that Kirk wouldn't recognize his new ensign as the gangly barely-a-teen he'd met once more than a decade earlier.)
We're not exactly into wrist-slitting territory yet, folks.
Also the casting news that they're looking for someone to play the captain of a starship strongly suggests that this is not going to be an "all Academy" movie. Presumably the group is going to go out on a training cruise much like that depicted in
The Wrath of Khan, which would be a nice bit of continuity.
I still think the best thing for the franchise would be a total reboot
a la Battlestar Galactica, as JMS suggested all those years ago, but this doesn't seem that horrible an alternative based on what's been revealed so far.
Regards,
Joe