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.
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 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.
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.
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.
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.
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.
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.
Daenerys Targaryen could also be a main character in an emperor - like role. She already had a strong claim to the Iron Throne and was a powerful leader. In a fanfiction, she could fully embrace her role as an all - powerful emperor, perhaps even uniting the Seven Kingdoms under her rule in a more forceful way than in the original series.
Maybe an outcast noble. They've been shunned by their family for their interest in the dark arts. So, they embrace necromancy fully and aim to use it to take revenge on those who wronged them. They start by raising the dead of their family's enemies, and gradually build an army of the undead. Their journey would be filled with self - discovery and moral quandaries as they delve deeper into the world of necromancy.