One idea could be exploring the backstory of the psychic powers in more detail. For example, how did the main character first discover her powers? Another could be a time - travel plot where the princess goes back in time to change an event that had a major impact on her kingdom. Maybe she tries to prevent a war or save a loved one from an early death.
You could write a fanfiction where the Psychic Princess loses her powers for a while. This would force her to rely on her other skills and the help of her friends. It could be a story of self - discovery as she realizes that she is more than just her powers. She might also meet a mysterious character who claims to be able to restore her powers, but at a great cost.
A plot idea could be a cross - over with another popular fantasy world. The Psychic Princess could find herself in a different realm, like a magical forest filled with strange creatures. She would have to use her psychic abilities to navigate this new world and find a way back home. Or, there could be a plot where she has to train a new group of psychics to defend the kingdom against a powerful dark force.