Steward of Solidarity

If an exerted creature is already untapped during your next untap step (most likely because it had vigilance or an effect untapped it), exert’s effect preventing it from untapping expires without having done anything.

If you gain control of another player’s creature until end of turn and exert it, it will untap during that player’s untap step.

You can’t exert a creature unless an effect allows you to do so. Similar effects that “tap and freeze” a creature (such as that of Decision Paralysis) don’t exert that creature.