Lawful GM

1. The PCs arrive at a new community and are selected for jury duty. However in this community jury duty is perilous. There is a legal dispute between two parties, and the community selects two juries for each party. The juries must fight to the death to determine which party wins the dispute. People can quit their jury, most do, because who wants to serve on a jury. It falls to the parties to convince their jurors to fight for them, with either money or pleading their case. The PCs could be divided between the two parties, which for optimum effect should be a wealthy guilty party and a less influential victim. The wealthy party is working to stack its jury with experienced fighters while the victims are struggling to keep their jurors from abandoning them.

2. This isn't so much an adventure idea but a means of introducing a NPC to the party. The PCs arrive at a new community and see numerous people in stockades outside of town (or perhaps locked up in a VR simulation). The PCs are informed they can pay the fines owed by the criminals in exchange for their indentured servitude for a month. You can come up with all manner of crimes they have committed, though none of them should be that serious, yet for some reason no one has come to pay their fines leaving them in the stockades.

3. There is a budget crisis. Perhaps the treasury has been stolen, the tax collectors are on strike, or the Interstellar Banking Empire has cut off credit to the planet. The PCs, and probably numerous other groups, are sent out to secure funds for the government. This could mean killing dragons and taking their hoards or executing a complex heist against the Interstellar Banking Empire. The government will offer the PCs a commission off all funds they raise and perhaps depending upon the situation a full pardon for past crimes.

4. An important vote is coming and the PCs are hired to protect a politician who will be casting one of the deciding votes. No one knows which direction he will go and the PCs may be able to sway him in one direction or the other. The problem is that both factions of the dispute don't want to risk him voting for the other side and have sent assassins to eliminate him. Perhaps one of the two factions kidnaps a member of his family to force him to vote for their position. The PCs need to keep him safe right up to the vote, which is compounded by his dysfunctional family that adds all sorts of complications to the politician's life and the efforts to protect him.

5. The PCs arrive in a community where the people spontaneously name one of the PCs as the community's leader. The PC is brought to the home of the community's leader, which is dusty and looks as though it hasn't been used in years. The community lavishes the PC with gifts and brings disputes for him to solve. He signs various documents and a great celebration is planned. The truth is the community is cursed that every three years a deadly evil comes to kill the community's leader as punishment for a crime the community committed many years ago. The evil will kill someone in the community so they have embraced a strategy of appointing an outsider as leader a few days before the evil comes.

6. The PCs are recruited to help the government with propaganda. They are sent to a remote province to discover who is smearing the government and to try to regain the people's trust in the province. It is actually the provincial governor who is secretly working against the government as part of a plan to form an independent kingdom. The governor will put on the appearance of trying to help the PCs while undermining their efforts and revealing them to radical groups that will attempt to kill them as agents of the government.

7. The PCs are sent to negotiate a treaty with a neighboring state. When they arrive it's very little negotiating as the ruler of the state instead wants to go adventuring with the famous PCs. The ruler is difficult and secretly orchestrates difficulties for the group to test the PCs. If he is pleased with their character he will tell them to come up with fair terms for the treaty that he will sign.

8. The PCs are sent to convince a noble to abdicate. The noble is quite old and his mental faculties have deteriorated. There is no clear succession and it falls to the PCs to determine who among his heirs should inherit his title. They will need to get the support of various political factions within the dominion for their actions to succeed. The noble isn't going to give up easily and his heirs will launch their own plots to discredit one another and win the support of the PCs. The deeper the PCs dig the messier the situation with no clear choice as who should be the next noble.

9. The PCs are hired by a unseen employer to discover secrets about a powerful politician. The PCs have to infiltrate the politician's life to discover his various secrets, which can be as mild or extreme as the GM desires. The PCs will report back to their employer who will reveal himself as the politician they were investigating, who wanted to assess his vulnerabilities, who he can and can't trust among his inner circle, ahead of various bold machinations he is planning. He will pay the PCs and offer to put them on retainer to investigate his many rivals within the government.

10. There will soon be protestors marching on the capital. The government has learned that paranormal forces controlled by foreign elements intend to disrupt the protests and the PCs are sent to stop this from happening.

There's lots of ways to use law and politics to inspire you with ideas to entertain your players. The trick is to watch the news with an eye for drama that you can twist and import into your campaign.