Maybe the hawk has some special powers. For example, it can sense dark magic approaching. Harry then has to protect the hawk while also relying on it to keep himself and others safe. The hawk could also form a bond with Harry that allows them to communicate telepathically, which would add an interesting dynamic to the story.
The hawk could be initially shy around Harry's friends. But as time goes on, it might start to trust them. For example, Hermione might study the hawk's behavior and try to teach it some simple tricks. Ron, on the other hand, could be a bit scared of it at first but later grow to like it when he sees how useful it can be.
A really interesting plotline could be set in a post - war scenario. Fleur, who has always had a crush on Harry, decides to actively pursue him. She starts by sending him anonymous gifts, which Harry is very curious about. When he finally figures out it's Fleur, they start to have conversations about the war, their losses, and slowly their relationship blossoms into something more than just a crush.
The plot could involve Harry using the trained hawk for various tasks like delivering messages secretly. Maybe the hawk helps him spy on the bad guys in Hogwarts, flying around unnoticed and reporting back to Harry.
One possible plotline could be that Harry, in a strange magical turn of events, is transformed into a small animal and Draco finds him. Draco then decides to keep him as a pet. Another could be that it's all part of a secret spell experiment where Draco has to take care of Harry in pet form to learn about empathy.
Maybe Dumbledore. He often has mysterious ways of providing Harry with tools or companions to help him in his journey. The trained hawk could be one such strategic gift from Dumbledore.
One interesting plotline could be Severus trying to protect Harry as his pet while hiding it from the other Hogwarts staff. For example, he might use magic to conceal Harry's presence when others are around, creating a sort of secret adventure within the castle walls.
Another plot could be centered around rivalry. The twin might be jealous of Hermione's popularity at Hogwarts. So, they start competing in various aspects, such as in Quidditch (even if Hermione isn't really into it, the twin could be). This rivalry could cause some tension between them, but eventually, they would realize that they are stronger together and reconcile.
In this fanfiction, the plot could be that Naruto's kid is kidnapped by an old enemy of Naruto's who wants to train the kid to be against the village. The kid has to use his wits and the little ninja training he has received so far to escape. Meanwhile, Naruto is on a desperate search for his child. This would create a lot of tension and also show how much Naruto has grown as a father compared to his own orphaned past.
Perhaps Voldemort uses magic to brainwash Harry into thinking he is his pet. Harry then has to fight against this false identity while still being under Voldemort's control. The plot could involve Harry slowly regaining his true self and using his new - found knowledge of Voldemort's inner workings (from being so close to him) to defeat him in the end. It would be a journey of self - discovery and resistance.
Perhaps Snape, in a moment of weakness or out of some deep - seated sense of responsibility, decides to protect Harry in an extreme way. He treats Harry like a pet in that he provides for all of Harry's needs but also restricts his freedom. This could lead to a lot of internal conflict for Harry, who is used to being independent. Meanwhile, Snape has to deal with the other characters in the wizarding world who might not understand his motives for treating Harry this way.