He might face political intrigue. There are likely those in the Wizengamot who oppose him due to his past actions and his association with Dumbledore. Also, he has to deal with the complex and often archaic laws and traditions of the wizarding world which could be a huge obstacle.
Well, in some fanfictions, Harry might gain control over the Wizengamot through his heroic deeds. For example, if he saves the wizarding world from a great threat again, the public support could be so strong that he can influence the Wizengamot's decisions. He could also use his knowledge of magic, especially some ancient or powerful magic that gives him an edge in the political arena of the wizarding world.
Hermione would likely be one of his allies. She's intelligent and has a strong sense of justice, always having been interested in the rights and wrongs of the wizarding laws. She could provide Harry with valuable research and advice.
The Weasley twins could be part of it too. Suppose Harry yells in excitement or anger about a new prank idea that the twins have come up with that might be a bit too dangerous. They could either encourage his yelling or try to tone it down, depending on their mood. And Malfoy might overhear Harry's yell and use it as an opportunity to taunt him, adding more conflict to the fanfiction.
In this fanfiction, Harry might also form alliances within the Wizengamot. He could team up with some of the more progressive members to counter the conservative forces. His skills as a wizard and his leadership qualities from his time at Hogwarts could come in handy in the political arena of the Wizengamot. He could even start initiatives to improve the relations between the wizarding world and other magical creatures, which would be a significant step forward in the world of Harry Potter fanfiction.
He becomes more politically aware. Through his experiences in the Wizengamot, he starts to understand the power dynamics and the behind - the - scenes workings of the wizarding world. His character evolves from just a hero on the battlefield to a political figure.
Maybe Albus has done something dangerous or disobeyed Harry's instructions. For example, if Albus got involved with some dark magic related stuff without Harry's knowledge, that would surely make Harry yell at him.
Maybe she's yelling at Ron. Their relationship in fanfictions can be quite complex. If Ron says something insensitive or does something stupid, like forgetting an important task that could put their mission in jeopardy, Hermione would surely yell at him.
Perhaps in a 'harry potter yells fanfiction', Harry yells when he discovers that someone has been spreading false rumors about his friends. He could be in the Great Hall, stand up, and yell at the perpetrator, creating a big scene full of drama and conflict within Hogwarts.