There can be many types of scenario, depending on what's his actual relationship with the kingdom he rules, its people and the royal court. For the royal court in particular, the presence of influent characters can do much, depending on the fact that they are secretly or openly on or against the side of the prince.
For example, as soon as news of the missing prince reach the court, Klathos the vizier, secretly longing for the throne, plays the part of the grieved mentor and dispatches a search-and-rescue team to go find the prince. In truth, that team has orders from him of bringing back evidence of the prince's death, so that Klathos' path to the throne is clean. If the team never returns (supposedly killed by the prince in a self-defense fight), maybe a second one will be sent by maintaining the face of "let us try one last time to find the dear missing prince", together with some skilled assassin.
But that's just one of countless possibilities.