If attached to an opponent’s creature, you can untap their creature during your turn.

Instill Energy’s untap ability will not untap the creature until it resolves. This means other spells and abilities can be used before it actually becomes untapped.

Any Auras (or other effects) which are on the creature that would cause it to not be untapped (or have a cost to be untapped) during untap step do not in any way hinder or imply a cost to use this card’s ability to untap once during the turn.