There might be some fanfics out there that combine these elements. However, finding one can be a bit of a hunt. You could also join some Harry Potter fan communities and ask if anyone has come across a fanfic with a Hungarian Horntail, Harry, Hermione and this Morrigan character. Maybe someone has a great recommendation.
It could be an action - packed adventure. Harry and Hermione might be facing the Hungarian Horntail in a new situation, and Morrigan could be a mysterious figure who either helps or hinders them. Maybe she has some ancient magic knowledge that could be useful against the dragon.
Often, it's portrayed as extremely menacing. Its size and strength are emphasized, with its huge wings and long tail being described in great detail to create a sense of awe and fear. For example, a fanfic might describe the ground shaking as it lands.
The Hungarian Horntail is one of the most fearsome dragons in the Harry Potter series. In fanfiction, it often takes on even more complex and interesting roles. Writers might explore its backstory, like how it came to be in the Forbidden Forest or what its relationship with other magical creatures is. It can be a great antagonist, with its powerful fire - breathing and sharp horns, adding a lot of danger and excitement to the story.
One idea could be to write about a young wizard's first encounter with the Harry Hungarian Horntail. Maybe he's a new dragon keeper at Hogwarts and has to learn how to handle this very dangerous dragon. It could be full of action as he tries to avoid its fiery breath.
One interesting 'Harry Potter Hungarian Horntail' fanfic could be one where the main character has to train a young Hungarian Horntail. It might show the unique bond that forms between the trainer and the dragon, different from the typical fear - based relationship in the original series. Another could be a fanfic that focuses on the history of the Hungarian Horntail in the wizarding world, exploring its origin and how it came to be such a feared creature. There are also fanfics that might put Harry Potter in a situation where he has to face multiple Hungarian Horntails at once, adding more danger and excitement to the story.
One interesting fanfiction could be about a young wizard's encounter with the Hungarian Horntail outside of the Triwizard Tournament. Maybe the wizard has to use unique spells to calm the dragon instead of fighting it.
In some fanfictions, the Horntail and Harry might have a telepathic connection. This allows Harry to understand the dragon's thoughts and motives, and they work together to uncover secrets in the wizarding world. For example, they might find a hidden chamber that holds a powerful magic item that could change the course of the war against Voldemort.
I'm not sure about a specific 'Harry has a Hungarian Horntail' fanfiction. But you could search on Archive of Our Own. There are tons of Harry Potter fanfics there, and you might find one with this unique concept.
You can start by creating a vivid setting. Maybe the story takes place in a hidden valley near Hogwarts where the Harry Hungarian Horntail has made its lair. Then, introduce a conflict. It could be that the dragon's lair is in the path of a new magical construction project at Hogwarts, and the school has to deal with it without harming the dragon.