Yes, there might be. The world of fanfiction is vast and diverse, and it's not uncommon for people to create crossovers like this. Writers often like to blend different fictional universes to create unique and interesting stories.
One idea could be that the Headless Horseman somehow finds his way into the wizarding world of Harry Potter. Maybe he's chasing a dark wizard who has escaped into Hogwarts. The students could be both terrified and intrigued, and Harry and his friends would have to figure out how to deal with this otherworldly being.
Maybe Harry gets cursed and turns into the Headless Horseman for a while. He has to figure out how to break the curse while still dealing with the normal Hogwarts stuff like classes and Voldemort threats.
Nick could teach Harry Potter through storytelling. Since he has been around for a long time, he must have countless tales to tell. He could use these stories to teach Harry about magic, its history, and the values of the wizarding world.
I'm not sure specifically as I haven't read it. But generally, a Harry Potter fanfiction could be about various things like a new adventure of Harry and his friends, an alternate timeline, or a different take on the magical world.
He could be a manifestation of a boggart for some students. For example, Neville Longbottom, who is often afraid of many things, sees the Headless Horseman as his boggart. Harry then helps Neville face his fear by teaching him a special spell. This would bring an interesting Muggle - wizarding world connection to the story. Also, the Headless Horseman's appearance could be related to some dark magic that is seeping into Hogwarts from the nearby Muggle areas.
Well, if Harry Potter were taught by Nick in a fanfic, it would likely be a departure from the normal curriculum. Nick might focus on teaching Harry about the afterlife in the wizarding world, something not really covered by other teachers. He could introduce Harry to the ghosts of famous wizards and witches from history, and how they still interact with the living world. This could open up new magical theories for Harry to explore, and perhaps even give him some advantages in dealing with the dark forces, as he'd have a deeper understanding of the spiritual side of magic.
As a Hogwarts student in a Harry Potter fanfic, Nick Burkhardt would bring a whole new dynamic. His understanding of the 'dark' side of creatures could be used in Defense Against the Dark Arts classes. He might not be the best at Potions or Transfiguration, but his unique skills would make him stand out. He could also have a rivalry with some of the pure - blood students who look down on his different background. However, his loyalty and determination would eventually earn him the respect of most of the Hogwarts community.
I don't know for sure without reading it, but it's likely to include Harry Potter himself, as it's a Harry Potter fanfiction. He's usually the central character in most such works.
If Nick Fury visited Hogwarts, he would surely be intrigued by the castle's defenses. He might compare them to S.H.I.E.L.D.'s security measures. The magic that protects Hogwarts, like the anti - Apparition jinx and the moving staircases, would be both fascinating and a bit of a headache for him as he tries to navigate the place.