It could be a Targaryen descendant. Since the Targaryens were known for their connection with dragons, it would make sense for one of their descendants to be the main character in a story about the last dragon.
A young girl from a small village near the Wall could be a great main character. She could be an orphan who has a special connection with nature. One day, she finds a dragon egg while exploring a cave. She has no idea what it is at first, but she feels drawn to it. As she takes care of the egg, she starts to develop powers of her own that are related to the dragon's magic. Eventually, she hatches the dragon and becomes a powerful figure in the North.
It could be about the last dragon in Westeros rising to power. Maybe it forms a bond with a new character who tries to use its strength to claim the Iron Throne. This person might face many challenges from the remaining great houses who don't want a dragon - backed ruler.
Daenerys Targaryen would be an obvious choice. Since she was the 'Mother of Dragons' in the original series, her return or a continuation of her story in a fanfiction where the dragons come back would be very fitting. She could have new adventures and use the dragons to reclaim her rightful place on the Iron Throne or to bring justice to Westeros.
A Skagosian outcast. He could have been banished from his tribe for some reason, like not following their brutal traditions. This character would be interesting as he would be an outsider even in his own land at first, and his journey to either regain his place or find a new one could be full of adventure and self - discovery.
Bran Stark could also be the main character. His new powers as the Three - Eyed Raven give him a whole new perspective. He could be the one to guide Westeros into a new era. He could use his knowledge of the past and his ability to see things that others can't to make decisions that would shape the future of the Seven Kingdoms.
Melisandre could be a main character if you consider her as a kind of warlock. She has her strange powers, like seeing the future in the flames. You could write a fanfiction exploring her past, how she became a red priestess and gained her powers, and her further adventures in Westeros, perhaps with her using her powers in different ways than in the original series.
Arya Stark could be an interesting main character as a summoner. She already has a lot of skills like stealth and combat. If she were a summoner, she could summon the spirits of those she has killed to either help her in battles or to gather intelligence. It would be a new twist on her character.
It could be a young apprentice wizard who has just discovered his powers. He is eager to prove himself and protect the North from all the threats it faces.
Perhaps a young knight who is given a lordship as a reward for his heroism in a great battle. He is inexperienced in ruling but has a strong sense of justice. He has to learn quickly how to manage his lands, deal with political intrigue, and protect his people from bandits and rival lords. He is also a bit of a romantic, and his love interest could be a lady from a neighboring house, which adds another layer of drama to his story.
Maybe it's a bastard son or daughter of a powerful lord. In the world of Westeros, bastards often face discrimination, but this one could be different. They might have discovered some evidence or a loophole in the laws of inheritance that makes them a legitimate claimant. Their story could be about fighting against the stigma of being a bastard while trying to claim their rightful place.