Princess was a noble title held by a female individual of royal blood, the daughter of a King and Queen.
In 2366, during a Tanugan trial of William T. Riker, a reconstruction of Manua Apgar's memories included Riker remarking that she must be lonely like a princess in a very high tower. (TNG: "A Matter of Perspective")
Patrick, whilst analysing a speech by Damar, theorised that a role akin to a princess existed in the intrigue of Damar's life, a role which Julian Bashir identified as Ziyal. (DS9: "Statistical Probabilities")
Furthermore, in a deleted scene from "Cost of Living", Deanna Troi recalled how her mother once dressed up as a Koropian princess.