You can absolutely do stuff like that. Maybe your party were awarded noble titles by the king for service to the crown. Then one day, when they're hanging out at their new keep, a messenger comes by with a court summons because they haven't been paying their taxes. Now they have to investigate the tax law, figure out what they owe, why they didn't know about it, and what they have to do now. And now you can go into a Robin Hood arc, where the players discover that this kingdom's tax system is super messed up, and preys on the poor and uneducated, and you have the added complexity of, your players are lords now, will they want to rock the boat in this kingdom that likes them? They're adventurers, so they can probably afford to just pay the ridiculous taxes, but that would mean leaving every other victim to their fate

Yeah, you get it.

For session one with a group that hadn't played together before, the party was getting together at a sort of Adventurers for Hire placement agency. They all had to take a number and then they would have an interview with HR. Basically, a one-on-one introduction with each player, asking a bit about their background, special skills, etc. It was a good ice breaker, and a familiar enough situation that really got the roleplaying going.

The wizard showed up far too early and got ticket 1, The rogue showed up around the expected time and got ticket 3, and the barbarian was very late and got ticket 43. After the wizard has their interview, they call for number 2, who is a rando halfling NPC. The rogue decides to lie his way through to cut in line and says he has ticket number 2.

The halfling was miffed, but like, whatever, halflings are used to being looked down on (pun intended) and figures he'll just explain and take the next interview. Well, the barbarian saw this exchange, and bullies the halfling into giving up their ticket. The barbarian takes the next interview, and by then all the vacancies were filled and the halfling was left out in the cold.

That halfling became a recurring character, someone who the party kept accidentally stepping on. Like, one time the party was at a fancy restaurant, and someone was given the wrong food, so they made a mild complaint. Well, the halfling made the food and was on his last warning, so the owner fires him on the spot. Poor guy, the party never did take the trouble to learn his name.

There's a quest like that in the recent Rogue Trader crpg, in which you help a party member obtain a permit from the Administratum.