Some dark wizards who were in hiding during the main battle might emerge. They could see the post - battle chaos as an opportunity to gain power.
He might focus on rebuilding Hogwarts. After all the destruction, it would be a huge task and he could use his influence and skills to bring it back to its former glory.
It could be a powerful veela who has a grudge against Hogwarts. Maybe a Hogwarts student in the past wronged her family. She uses her charm and powerful magic to try and bring chaos to the school. She first lures some of the male students with her beauty and then uses them to carry out her devious plans. For example, she might make them steal important magical artifacts from the school that are used to keep Hogwarts safe.
In many fanfics, Harry Potter might become an Auror after Hogwarts, using his skills to fight dark magic. He could also start a family with Ginny and raise their children in a world that's gradually recovering from the war.
In the 'harry potter after hogwarts fanfic', a really interesting plot could be about the discovery of new magical creatures or lost spells. Harry, being the adventurous type, might go on quests to explore these new elements. He could also get involved in international wizarding relations, using his fame and experience to bridge gaps between different wizarding communities around the world. This would open up a whole new world of magic for the readers to explore.
Luna Lovegood could be a main focus. Her unique perspective on magic could be used to discover new magical phenomena that emerged after the battle. She might also be helping the other students deal with their post - battle stress, using her calm and dreamy nature to soothe them.
Obviously, Harry Potter himself would be a central character. Ron and Hermione, his closest friends, would also likely be in it. Ginny, as Harry's love interest, would probably play a significant role too. Other characters like Neville, who has grown into a strong wizard, could also be featured. And of course, we might see some of the old Hogwarts professors, perhaps McGonagall still guiding the school in some way.
Another possibility is McGonagall again. She has been an excellent teacher and deputy headmistress for a long time. Her experience and strict but fair nature would ensure the smooth running of Hogwarts. She already has a great relationship with the students and faculty, and could continue to uphold the school's traditions while also making some positive changes.
It could be a group of rogue Death Eaters who have formed their own empire after Voldemort's fall. They might be more radical and have new, even darker plans for the wizarding world.
There could be alien dark wizards. They might have their own brand of magic that is different from what Harry is used to on Earth. They could be trying to steal Earth's magic for their own evil purposes.
There could be a group of powerful and ancient magical creatures that have been awakened or angered. For example, a clan of centaurs who feel that wizards have violated their territory too many times. They gather their forces and declare war on the wizarding world, and they would be new and unexpected villains in the story.