Definitely Harry Potter himself. His ability to stand up to great evil would be interesting in the cutthroat world of Game of Thrones. He could be a force for good against the likes of Joffrey Baratheon or Ramsay Bolton.
Harry Potter and Jon Snow would be a very interesting pair. Harry is used to fighting against dark magic and Jon is a natural leader who has faced many challenges in Westeros. They could learn a great deal from each other. Harry could teach Jon about magic and Jon could teach Harry about leading in a world without magic but full of political scheming.
Jon Snow would be an interesting character in a 'Game of Thrones' and 'Harry Potter' crossover. He has a strong sense of duty and honor, similar to some of the characters in Harry Potter. He could be introduced to the concept of magic and might be skeptical at first. But as he sees the power of magic, he could use it to better protect the North. He could also learn from the wizards about different ways of leadership. And his relationship with the direwolves could be explored in new ways, especially if there was some sort of magical connection between them and the magical creatures in Harry Potter's world.
Arya Stark would be really interesting. She could have a Zoroark as her Pokemon. Zoroark can change its appearance, which would be useful for Arya's skills in disguise. Also, Jaime Lannister could be paired with a Lucario. Lucario is a noble and powerful Pokemon, much like Jaime's complex character.
I think Ragnar and Tyrion would make an interesting pair. Ragnar is a fearless and shrewd leader, while Tyrion is intelligent but often underestimated. Their interactions could be full of banter and strategic discussions.
I think Tyrion Lannister would be very interesting. He's already a clever character in Game of Thrones. In a fanfiction with Harry Potter, he could learn magic and use it in his devious plans. He might even go to Hogwarts to study magic and cause all kinds of chaos there.
Arya Stark and Castiel. Arya is a skilled assassin with a thirst for revenge. Castiel is an angel who often struggles with understanding human emotions. Their interactions could be really fascinating. Castiel could help Arya understand the deeper spiritual side of her revenge, while Arya could teach Castiel about the importance of personal vendettas in the context of the cut - throat world of Westeros.
Arya Stark is very interesting. She goes from a young girl to a skilled assassin. Also, Tyrion Lannister with his sharp wit and being an outcast in his own family is quite engaging.
Black Widow. She's a master spy and assassin. In the world of Game of Thrones, she could easily blend in with the various spies and informants. She could play the game of thrones better than most of the characters there, using her charm and combat skills to manipulate the situation to her advantage. She might even be able to uncover some of the deepest secrets of the Seven Kingdoms.
Jon Snow would also be a great addition. His journey from being a bastard to a leader in Game of Thrones could be paralleled in the world of Frozen. He could learn from Elsa about controlling his powers (if we assume he has some new ice - related powers in this crossover) and in turn, teach the people of Arendelle about loyalty and sacrifice, which are values he has held dear in Westeros.
Arya Stark in a 'Naruto Game of Thrones crossover fanfiction' would be fascinating. If she were to learn some of Naruto's ninja skills, she would become an even deadlier assassin. And Naruto's influence might change her path a bit, making her less vengeful and more about bringing real change to Westeros.