She could be a maester - like figure. With her vast knowledge, she could advise rulers on various matters, from war strategies (using her strategic thinking from Hogwarts battles) to matters of health and economy. She'd be different from the traditional maesters as she has a more modern - thinking approach.
Hermione might become a sort of rebel leader. Given her penchant for fighting against injustice in the wizarding world, she'd likely oppose the corrupt systems in Westeros. She could gather a group of like - minded individuals, including smallfolk and disillusioned nobles, and start a movement for change. She'd use her intelligence to plan their actions and her magic (adapted to the Game of Thrones world) to protect them.
In a Game of Thrones fanfiction, Hermione might play the role of a disruptor. She's not from that world and has different values. Her presence would disrupt the status quo. For instance, she would not tolerate the way women are often treated in Westeros. She'd speak up and fight for equality, which would put her at odds with many of the traditional lords. At the same time, her magical abilities would make her a force to be reckoned with, so she could start to change things whether the people in Westeros like it or not.
She could use her intelligence to navigate the complex politics of Westeros. For example, in King's Landing, she could outwit the likes of Cersei. Hermione's knowledge of magic could be translated into a form of sorcery in the Game of Thrones universe, giving her an edge in battles or in solving the many mysteries that the land holds.
In a Game of Thrones fanfic, Hermione could be a mediator. There are so many conflicts in Westeros, from the Stark - Lannister feud to the battles for the Iron Throne. Hermione, with her logical mind and ability to see different perspectives, could step in and try to broker peace deals. She would use her communication skills, honed in the wizarding world, to get the warring parties to at least listen to each other and consider alternatives to all - out war.
Hashirama might become a powerful ally or a feared enemy in the Game of Thrones fanfiction. If he aligns himself with a certain house, his powers would make that house very difficult to defeat. He could also be a lone wanderer, using his skills to help the common folk. For instance, he could use his wood - style jutsu to create shelters for the poor or to clear paths in the forest for travelers. He would be like a force of nature in the world of Westeros, disrupting the normal power dynamics.
Aragorn's character arc could involve him initially being a reluctant participant in Westeros' affairs. But as he discovers the true nature of the threats like the dragons or the White Walkers, he transforms into a more active and determined figure. He could go from being a lone wolf to a leader who unites different factions against a common enemy. Along the way, he might also have to deal with his own inner demons and the differences in culture between his homeland and Westeros.
With Arya Stark, Achilles could be a mentor - like figure. Arya is on her journey to become a great fighter, and Achilles, with all his battle experience, could teach her new techniques and a different perspective on combat. However, their cultural differences, Achilles from Greek mythology and Arya from Westeros, could also create some interesting clashes and learning opportunities for both characters.
She could make a spell - powered communication device. This would be like a magical version of a smartphone. It could allow wizards to communicate instantly across long distances, even in places where normal communication spells don't work. It would be a great invention considering how often wizards need to communicate in the wizarding world.
One possible character arc for Merlin could be that he starts as an outsider, just like in his original story. He comes to Westeros and has to learn about the different cultures and politics here. As he gets more involved, he realizes the importance of using his magic for good in this new and dangerous world. He might start by helping the smallfolk, and then gradually get involved in the bigger power struggles, all the while maintaining his sense of right and wrong.
She could be a powerful sorceress. In the world of Game of Thrones, magic is a mysterious and dangerous force. Bella might be someone who has been secretly studying magic, perhaps in the far reaches of Essos. She could use her powers to manipulate the political situation in Westeros, for example, by influencing the minds of the lords and ladies during their councils. This would add a new and interesting dynamic to the complex web of power struggles in the series.
One possible plot could be that Hermione, with her intelligence and magical skills from the Harry Potter universe, is transported to the world of Game of Thrones. She meets Jamie there. Maybe she tries to use her knowledge to prevent some of the bloodshed in Westeros. She could team up with Jamie, who has his own complex history and skills with a sword. Together they might try to bring about a more peaceful solution among the warring houses.