Perhaps the hawk was a gift from a mysterious figure. Harry then has to train it further to perform more complex magic - related tasks. It could be used to find hidden magical objects. The hawk might have special abilities that assist Harry in his adventures against dark forces.
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.
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.
It could be about Sirius teaching Harry advanced magic skills like Patronus charm. Sirius, being a skilled wizard, might train Harry to be better at dueling and facing dark wizards.
Well, perhaps it could be about Merlin using his ancient and powerful magic to train Harry in combat skills. Maybe he teaches Harry spells that have been long forgotten.
Well, it could be that Merlin teaches Harry some ancient and powerful magic. Maybe Merlin shows Harry how to control magic in a more instinctive way, different from what he learned at Hogwarts.
One possibility is that Harry discovers a world where fanfiction has the power to change the real wizarding world. So he has to train to fight against the alterations caused by these fictional stories. For example, if a fanfiction made Hogwarts a place full of dangerous magical beasts that don't belong there, Harry would need to train to restore order.
Well, perhaps Harry could be trained in some long - lost or dark magic that Dumbledore has been hiding from him. This new training might make him even more powerful than before, able to defeat Voldemort in a more spectacular way.
Maybe Harry discovers some long - lost magic techniques taught by Godric. He could become super powerful and use ancient spells to fight Voldemort.
Well, in this fanfiction, it could be that Hephaestus trains Harry Potter to have a better understanding of the more physical and mechanical aspects of magic. For example, he might learn to build magical devices that can be used in battles or for other important tasks. This would give Harry an edge over his enemies as he'd have skills that no other wizard has. It could also lead to new alliances as other wizards might be interested in his newfound abilities.
Well, perhaps in this fanfiction, Harry discovers he has an affinity for snakes early on. Maybe he's able to communicate with them in a deeper way than Parseltongue allows. The snakes could train him in stealth and survival skills, like how to move quietly in the Forbidden Forest or find hidden passages. They could also teach him some unique magic that is related to the ancient magic of serpents.
Maybe it's about Harry learning some advanced magic spells from Flitwick. Flitwick could be teaching Harry unique charms or how to use his wand more effectively.