Depth Psychology: A prince stands for masculinity, knowledge, and intellect: you are either looking for such a man, or you could nurture these qualities in yourself. Dreaming about a princess: you might be repressing, maybe unconsciously, your feminine side, your compassion, and your feelings in general.
If you are a man, are you looking for a female partner who is “better” than so-called ordinary women—maybe in appearance, heritage, upbringing, education?... Dreamers Dictionary
For a male, to see a princess in his dream symbolizes an important female in his life, such as a sister. It portrays his idea of an ideal woman.... Dream Symbols and Analysis