A new character could be a demigod who has the power to control time in small bursts. They could be from a really old and secretive family of demigods that no one knew about. This character could cause a lot of chaos or be a great help to Percy depending on their motives.
Maybe an elf - like creature that lives in the forest near Camp Half - Blood. This creature has a special connection to the nature spirits and can communicate with them. It could befriend Percy and help him understand more about the natural magic that exists in the demigod world.
There could be a rogue godling, a child of a minor god who has been cast out by the other gods. This godling has a grudge against the major gods and tries to use Percy as a tool to get revenge. But as Percy gets to know this godling, he discovers that there's more to their story and tries to help them find a new place in the world of gods and demigods.
A new demigod from a previously unheard - of god or goddess. Maybe a child of a minor deity who has some unique powers that could either help or hinder Percy in the situation of the collapse. For example, a child of Hypnos who can manipulate sleep and dreams, and their powers could be used to either give Percy visions of how to fix things or put him in a dangerous trance.
A new demigod from a really rare godly parentage, like a child of Hypnos, the god of sleep. This character could have unique powers related to dreams and illusions and could be an ally or an adversary to Percy. Another could be a centaur who has been exiled from his herd for some reason and has a vendetta against the Olympians. He could be a source of knowledge for Percy about some of the more hidden secrets of the gods.
There could be new demigods. Maybe some who were hidden during the giant war and now come out. For example, a demigod of a less - known god or goddess.
A group of rogue demigods who have been using vapor travel to steal from other realms. They could be both enemies and potential allies depending on the situation. They might have unique powers related to vapor manipulation that Percy and his friends have never seen before.
A mermaid - centaur hybrid could be a really cool new character. This character could have the upper body of a centaur and the lower body of a mermaid. They could be an expert in both land and sea magic, and help Percy on his quests. They might also have a mysterious past that is related to the ancient wars between the gods.
Percy Jackson is likely still one of the main characters. After all, he's the central figure in the original series. And Annabeth might also be there, as she's always been by Percy's side.
A centaur who has lived in both the Roman and Greek territories. He could be a mentor to Percy, teaching him about the similarities and differences between the two cultures' ways of combat, magic, and survival. He could also have a lot of stories about the ancient times when the two cultures were more intertwined.
There could be a new neighbor in Jenna's apartment building. A quirky artist who inspires Jenna in new ways, either in her personal life or her career at the magazine.
Obviously, Percy would be one of the main characters. Annabeth might also be there, as she is Percy's close friend and often involved in his adventures.
Well, there could be new demigod children of Hades. Maybe a girl who has the power to control the shadows in a unique way, like she can use them to create portals to different parts of the underworld. Or a boy who can communicate with the dead in a more advanced way than the usual children of Hades, and he has some sort of prophecy related to Percy.