The Mountain of Aaron, Jabal Harun, is one of the great hikes around Petra: a long, exposed climb to the white-domed shrine traditionally associated with Aaron, brother of Moses. The reward is not only the religious site but the view back over Petra's broken sandstone country.
This is a serious excursion, not a casual add-on after the Treasury. Start early, carry water, and use local guidance if you are not confident with the route; the distance, heat, and isolation make it feel much wilder than Petra's main tourist corridor.