A prince was a royal title referring to the son of a monarch.
On Earth in the 20th and 21st centuries, Charles, the son of Queen Elizabeth II, was titled Prince of Wales. (Star Trek: The Eugenics Wars novel: The Rise and Fall of Khan Noonien Singh, Volume 2)
In the 23rd century, Raviki was a prince of Nukolee, the son of Emperor Djan and his wife. (TOS comic: "A World Gone Mad")
In the 24th century, Si Cwan was a prince of the Thallonian Empire until its fall in 2373. (NF novel: House of Cards)