This is not a common. Repeatable free Train effects seem too strong at common, especially because this affects other permanents. Note that every mechanic which involves getting +1/+1 counters over time (at common) only affects the creature that has the ability - Outlast, Evolve, Dethrone. Or, in the case of Bolster, Explore, and other keyword actions, all creatures that have that ability at common have it as a one-shot effect rather than a repeatable effect. This card, as with (((Tah-Crop Cook))), is more suitable at uncommon as is.

Not a fan of the "downside" clause either, especially since Fogwalker caused so much confusion during SOI draft, and exert is usually on creatures without vigilance. If my creature is training to the point of exhaustion so he doesn't untap, how come he can attack immediately after training?

You also might want to remove the "target" from the mechanic so the entire mechanic isn't red-flagged from the start at common. Maybe wording like this?

>Whenever ~ attacks, target creature trains 1. (Put a +1/+1 counter on it. It doesn't untap during its controller's next untap step.)

Train was originally designed to target untapped creatures but it works better? by being able to target anything. It's boring to just say put a counter on a creature so making them exerted was less boring and a little flavorful. Maybe it plays better than it's worded.

I am not a fan of hiding targeting restriction in the reminder text (even if Wizards did it themselves). So far the new wording for train is an upgrade.

The total lack of connection between the condition and effect on your creatures that train so far is lacking. You could focus all your training on one untapped creature left behind as a blocker and not even tapped and the exertion usually wouldn't matter at all.

Exert on original Amonkhet cards made sure it matters by exerting attacking creatures that usually tap at the same time.

This can also, weirdly enough, work as an anti-tech against undying cards.