For example, something like Act of Treason will be able to unap the Elite. And while it would cost a lot of mana, if the Elite were enchanted by a Crab Umbra, you could use the the ability of the Umbra to untap the Elite.
Arbalest Elite’s ability only prevents it from untapping at the beginning of a turn.
Arbalest Elite‘s activated ability deals three damage to an attacking or blocking creature. This ability has an additional effect that keeps the Elite tapped for a bit. This effect only applies to the Elite as long as it is the same permanent and it only prevents the Elite from untapping as normal in the untap step of a turn.