[Phantasm]

Well, there's not much to go on. However, I do have a few ideas:

As the mage is also the Prince of the Realm, the other two could conceivably be part of his entourage. This would make him suitable to be a diplomat to other nations, giving him Diplomatic Immunity in a lot of cases. This could lead to:

• A good old-fashioned murder mystery as he's visiting abroad where he's the prime suspect and must clear his name.
  
• There's a dragon/demon/Cthulhu-esque Horror terrorizing the landscape, slaughtering his kingdom's peasants, and in order to show that The King Really Cares For His People, he's sent his son out to either A) gather allies, or B) take on the beast himself. The smart move is to do A, but B is excellent for PR, if the peasants are starting to revolt.
  
• The Prince must find a woman suitable to be his bride, and the Royal Oracle, who is on the payroll of the Grand Duke, the King's younger brother and only other heir to the throne, has to quest through unknown lands to find her, possibly uniting his Realm with one from Far Off.
  
• Civil war has erupted in the kingdom, pitting his father's Royalist forces against the usurper's Puritans. The Prince is in exile, along with his two most trusted friends, after the King was publicly beheaded. (Yes, I took this from the English Civil War of King Charles I vs Oliver Cromwell. The English Civil War was TL5, not TL3, but the circumstances could be very similar.)