The Prince Outfit consists of a prince tunic and prince leggings. It can be acquired by trading a frog token from the Frogs random event to Thessalia of Thessalia's Fine Clothes. The outfit cannot be traded to other players or sold to general stores.
The Frog Event is available to both free-to-play and pay-to-play players. If you're RuneScape Character is female, then you will get a Princess Outfit for you Frog Token.