It could be a new character who has the ability to manipulate the game mechanics. This character might be able to change the rules of the game - like world they are in, which would make them very interesting.
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.
Perhaps a plot where the characters can use game-like powers to change the outcome of key events in the Harry Potter universe. For example, being able to redo a battle like a game level until they achieve victory.
I think it would be really interesting to focus on Hermione. Her thirst for knowledge would make her eager to learn about the world of Eragon, especially the dragon - riding and the different types of magic. She could also bring her logical thinking and problem - solving skills to the table, which would be very useful in both worlds.
It would probably be Harry Potter himself. He's from a world full of magic and mystery, and seeing him interact with the very real and regal world of the Queen would be fascinating.
Pairing Supergirl with Severus Snape could create a really dynamic relationship. Snape has his own dark past and complex personality. Supergirl could potentially see the good in him and try to bring it out. They could have a bit of a clash at first, with Snape being suspicious of her, but over time, they could develop an unlikely friendship or at least a mutual respect as they face common enemies in the wizarding world.
Definitely Dr. Strange. He already has a connection to magic, so in a Harry Potter x Avengers fanfic, he could bridge the gap between the two worlds. He could learn new spells from the wizards and share his knowledge of the mystic arts. His ability to manipulate time and space would be really useful in the wizarding world, and he could help the Avengers and the wizards deal with threats that involve both magic and science.
Hermione Granger would be a great choice too. Her thirst for knowledge would lead her to study the lore of the Highlanders intensively. She could figure out ways to use magic to either protect Immortals or find a way to end the immortality curse if she saw it as a danger. Her intelligence would make her a force to be reckoned with in the Highlander's world.
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.
It could be Harry Potter himself. Given all the hardships he faced in the original series, a second chance would open up a whole new world of possibilities for him. He could use this chance to prevent some of the tragedies that occurred, like the deaths of his friends or mentors.
Maybe it's a character who has been in the background in the original books but now gets their chance to shine. Like a house - elf who decides to break free from their servitude and start a new life. They could discover their own magical powers that were suppressed all this time and use them to create a whole new existence for themselves in the wizarding community.