No, and "Prince" is not a fixed title so there's not a single correct way to do this.
Vampire: The Requiem 2nd Edition mentions the following regarding the subject (p.75):
In the All Night Society, cities become city states. Their culture and boundary lines only illumine when the sun goes down. Vampire hierarchy often rises to an apex. This just comes naturally to predators. Often there is a vampire at the top, call her Prince or Boss or Exalted One or Bishop or President. Domains are authoritarian regimes, governments of tooth and claw and hyena laughter. Some princes are more openly brutal than others.
This would suggest that "Prince" is not the only thing the top vampire can call themselves (reminder that the word is derived from the Latin Princeps, "the first"). Meanwhile, the first edition of Vampire: The Requiem states the following (p.33):
While Prince is the most common term by far, Kindred leaders refer to themselves as Cardinal, Bishop, Archbishop, Don, President (usually in the case of those rare elections mentioned earlier), Sultan, Lord, Duke or whatever title strikes their fancy, depending on the nature of their government. A few self-styled “Queens” exist, but most Kindred leaders avoid use of the title King.
While the first edition is a lot more blunt about how this works, the second edition is a lot vaguer. This is in stark contrast with Vampire: The Masquerade where "Prince" is a fixed title with fixed responsibilities and powers, as are "Cardinal" and "Bishop" mentioned in the first edition Requiem book.
So how do you address a vampire Prince?
When writing a letter to a member of the British royal family who trace their lineage to the Queen and her consort the correct salutation at the top of the letter is "Your Royal Highness". But since (most) vampire Princes don't have such pedigree they are not Royal (and beware the Prince who calls himself King). "Your Highness" would be correct, but carries the risk of being seen as sarcastic. As such, "My Prince" would make for a good alternative: it states the ranks and one's subservience to the holder of said rank, without the risk of sounding catty.