Well, her friends would surely miss her a great deal. Harry and Ron would feel like they've lost an important part of their team. Academically, the Gryffindor house might see a decline in grades as Hermione was often the one helping others study. Also, the teachers might be disappointed as she was a brilliant student.
One possible reason could be that she's frustrated with the school's bureaucracy. For example, if she constantly faces obstacles in getting approval for new study groups or advanced classes. Another reason might be a personal quest. Maybe she discovers a hidden mystery outside of Hogwarts that she can't explore while being a student there.
She might become more distrustful. After being betrayed, it's natural for her to question the motives of those around her, even her closest friends.
One reason could be that she might be on a secret mission. In some fanfictions, she could be trying to find a powerful magical artifact outside the walls of Hogwarts to save the wizarding world from a new dark threat. She might believe that she can't achieve this while staying within the school's confines.
Maybe she leaves because of a conflict. It could be with a teacher who doesn't support her unorthodox ways of learning or a fellow student who makes Hogwarts an unpleasant place for her. In fanfiction, there could be a lot of creative interpretations of such conflicts.
It could lead to a lack of recognition. Without a top story, she may not stand out as much in a competitive environment.
One possible consequence could be a lack of public interest. If she's a journalist, for example, without a top story, she might lose credibility or readership. Her competitors could gain an edge as they have more engaging stories to offer.
The students would surely miss her. She's a role model for many, especially the younger students who look up to her intelligence and determination. Without her, the study groups and academic competitions might not be as intense or successful.
The relationships within the village would be severely affected. His friends would be heartbroken and split into groups, some trying to find him, others blaming themselves. The new generation of ninjas would also lack a role model. And the balance of power in the ninja world could shift, as other villages might see Konoha as weakened without Naruto and try to gain an upper hand.
It can completely change the dynamic. For one, it might lead to a new setting. Instead of the familiar Hogwarts corridors, the story could shift to different magical locations where Hermione is now exploring. This can introduce new characters and magical creatures.
One great Hermione Granger fanfic could be one that focuses on her academic achievements during her Hogwarts years. It might show her studying hard in the library, coming up with brilliant solutions to complex spells or potions. For example, she could be researching a new way to counter a dark magic spell that's been causing trouble in the wizarding world. Another could be about her friendships, like how she helps Neville gain confidence in his magical abilities.