A princess was a royal title referring to the daughter of a monarch.
In the 23rd century, José Tyler was romantically involved with a princess from Kalajia VII, though he refused to tell anyone. (TOS novel: Legacy) Kyanna was a Klingon princess. (TOS novel: The Starless World) Sharday was an Aarakian princess. (TOS - Year Four comic: "Issue 2")