Glorybringer

If a creature has a targeted triggered ability that triggers when you exert it, you can exert it even if there isn’t a legal target for that triggered ability.

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.

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.