Artemis could be a major character. As the goddess associated with the Hunt, she would have a huge role. She might initially be skeptical of Percy's ability to protect the Hunt but gradually come to trust him. Thalia, who is part of the Hunt, would also be important. She has her own history with Percy and could be a key ally in the protection efforts.
Annabeth could also play a role. She's Percy's close friend and her strategic mind could be very useful in planning how to protect the Hunt. She might offer different perspectives on how to deal with threats compared to Percy's more impulsive style. And maybe some new characters could be introduced, like a young and inexperienced hunter that Percy has to especially look out for during the protection process.
There could be some of the other hunters in the Hunt like Zoe Nightshade (if in a story that allows for her presence in some way). Her skills and knowledge of the Hunt's ways could be valuable. Also, Grover could be involved. He's Percy's friend and his connection to nature might come in handy when it comes to protecting the Hunt in areas related to nature and the wild.
There could be his friends or comrades in the hunt. For instance, someone like Annabeth who might be affected by his leaving and try to convince him to stay.
Artemis is a must - as the goddess leading the Hunt. Her hunters, especially those like Phoebe, could be main characters. Phoebe could be curious about Percy and his blindness. She might be the one to first approach Percy when he's found. Another character could be Chiron. He could hear about Percy being with the Hunt and come to check on him. He could offer advice to both Percy and the Hunt, based on his vast knowledge of demigods. And then there's the Oracle. It could give some cryptic prophecy related to Percy's new situation with the Hunt, which would add an interesting layer to the story.
Obviously, Artemis. She is in charge of the Hunt, and her relationship with Percy would be central to the story. Then there could be Zoe Nightshade. She was a very important member of the Hunt in the original Percy Jackson lore. If Percy is adopted by the Hunt, she would have a big influence on him, either as a mentor or as someone who initially opposes his presence. And the wolf is also crucial. It could be a mysterious figure, maybe a messenger of the Hunt or a guardian of some sort, and it would be involved in Percy's journey every step of the way.
Annabeth could be a main character. She might be skeptical at first about Percy's new ability to control Styx, but then she uses her wisdom to help him understand the implications and possible uses of it. For example, she could research ancient texts to find out if there are any hidden dangers or benefits to Percy's control.
There could be a rival within the family. Someone who wants Percy out of the way, perhaps for inheritance reasons or because they're jealous of Percy's abilities or popularity. This rival could be the one who instigates the events that lead to Percy's disownment. And then there might be a mentor - like figure outside of the family who takes Percy in after he's disowned and helps him to grow and face his new situation.
Grover could also be a main character. He might be at the scene when Percy gets drunk and try to use his nature - related powers to sober Percy up. Grover could also provide some comical relief with his reactions to Percy's drunken state, like his horrified expressions or his attempts to herd Percy like he would a wild animal.
Well, there could be a wise old wizard who discovers Percy. The wizard takes it upon himself to protect Percy from the forces that might be after him because of his mysterious origins. He becomes like a mentor to Percy, teaching him about the magical world and how to control his powers.
A young mermaid named Ariel could be a main character. She could be Percy's friend and help him explore the underwater world. She could teach him how to swim faster and find the best hiding places from the bigger sea creatures.
Nico di Angelo could be a central character. Given his connection to the underworld and his own complex relationship with the gods, he might be the one who has the most knowledge about what really happened to Percy and how to reverse it. He could be on a quest to bring Percy back from the dead, facing many challenges along the way.
There could be a new, made - up character. This character could be a seer who had foreseen Percy causing the earthquake but was unable to prevent it. Now, this seer has to work with Percy to understand why it happened and how to prevent future disasters. Or it could be a young demigod who looks up to Percy and is now caught in the middle of the chaos Percy has caused and has to learn to be brave and helpful during this crisis.