Per Ralph Breaks the Internet, you qualify as a princess if you meet even one of the following qualifications: magic hair, magic hands, animals talk to you, you were poisoned, cursed, kidnapped or enslaved, or if people assume all your problems got solved because a big strong man showed up.
So the question is, who outside of the established Disney Princesses fits this bill?
People often suggest Princess Leia - the clue is in the name, after all. However, I'd like to point out that none of the above requirements mention having to be female, and that Leia's father Darth Vader both has magic hands and was once a slave. Thus he is clearly a Disney Princess.
I'd also like to nominate Thor. Magic hair? Check - watch how he transforms his scraggly hair into a well-maintained and woven thatch in Avengers Endgame. Magic hands? Check - we see him casting lightning bolts from them in Thor Ragnarok. Animals talk to you? Check - he and Rocket have some good conversations. Cursed? Maybe check - Odin stripping him of his powers seems to fit in my opinion. Enslaved? Check - Grandmaster enslaved him. People think a big strong man showing up solves all his problems? Check - at the start of Avengers Infinity War many viewers assumed Thor's problem with Thanos was solved when the Hulk intervened. Thor qualifies on multiple counts, and so is a Disney Princess.
Any other unlikely candidates? Make your cases.