One idea could be that the new generation discovers a time - turning device left by Hermione. They travel back to the time of the first Triwizard Tournament. There, they meet a young Sirius Black and Remus Lupin, and get involved in the mystery surrounding Cedric Diggory's death in a new way.
One idea could be that the next - generation characters travel back to the time of the first wizarding war. They could accidentally change some small events, which then have big consequences on their present time. For example, they might prevent a certain spell from being cast that was crucial in the defeat of a dark wizard, and now they have to figure out how to fix it in their own time.
Well, in a time travel fanfic, perhaps Harry accidentally travels back to the time when the founders of Hogwarts were still alive. He might learn ancient magic directly from them and use that knowledge to defeat Voldemort in his own time. Or Ron could go back in time and end up changing some Quidditch matches in the past, which then has unexpected consequences for the present, like different teams winning championships and changing the overall Quidditch culture at Hogwarts.
One idea could be exploring the friendship between the children of different Hogwarts houses. For example, the son of a Gryffindor and the daughter of a Slytherin becoming best friends against all odds. Another could be a new dark threat emerging and the next generation having to use new spells and magic they've developed. Maybe they discover a hidden chamber in Hogwarts that has secrets about the founders that no one knew before.
Perhaps a story about a second - generation character who discovers a long - lost relative who was involved in some dark magic in the past. This character has to deal with the family secret while also trying not to let it affect their relationships with their friends at Hogwarts. They might be tempted by the power of the dark magic their relative was involved in, creating an internal conflict.
In a 'Harry Potter Dark Time Travel Fanfic', a character could travel back to the time of the first great wizarding war. They could attempt to save lives that were lost in that conflict, but in doing so, they unknowingly create new threats. For instance, saving a certain wizard might lead to that wizard being corrupted later and causing even more destruction.
Another idea is that Harry travels to a time when his family was being hunted by Voldemort but in a parallel timeline. He could try to find a way to merge the timelines in a way that saves his family in both timelines. This would involve a lot of complex magic and decision - making on Harry's part.
One idea could be that Harry travels back in time to his parents' era. He uses his mastery of death to protect them from Voldemort. Maybe he can't directly interfere but finds a way to subtly change things, like giving his father a special charm that ends up saving their lives in a crucial moment.
One idea could be that in this new order, Hogwarts starts accepting students from all magical creatures, not just witches and wizards. This would lead to a whole new dynamic in the school, with different cultures and magic types interacting.
Well, in a 'new normal' Harry Potter fanfic, perhaps the Ministry of Magic decides to open up more to the Muggle world in order to promote better relations. So, Hogwarts starts an exchange program with some Muggle schools. This would bring a whole new set of challenges and friendships. Also, the way Quidditch is played could change. Maybe there are new safety regulations for players, like wearing special protective charms all the time.
One idea could be the new marauders getting into trouble with a new set of magical artifacts that have been hidden in Hogwarts for centuries. They might discover a map that leads to these artifacts, much like the Marauder's Map. Another could be their interactions with the ghosts in Hogwarts in a more adventurous way, like trying to solve a mystery that the ghosts have been keeping for ages.