The king doesn't give a fig what's going on in the kingdom as long as he's got his ale and whores. He does not like when politics interfere with his revels and he can be rather brutal when it happens. The prince, an adult, has a pretty free hand but wants to avoid pissing off his overbearing father. The party is a small group of the princes drinking companions that the prince sometimes pays to solve his problems that threaten to rise to the level of annoying the king.
The prince has lately been cavorting in some of the villages and claiming the right of prima nocta in his father's name. A group of villagers has decided to put an end to it. They've started ambushing patrols and maybe even made an attempt to capture the prince himself. The party needs to find and eliminate these trouble makers before his father finds out.
This would be suitable for a low level party. If the players are higher level, switch it to the villagers having pooled their money and hired some adventurers of a suitable to take out the prince.