The goddess Hera might also be a great antagonist. Since she has a history of interfering in the lives of demigods, she could be jealous or threatened by Percy's rebirth. She might try to stop him from reaching his full potential in his new life or cause trouble between him and his new allies.
It could be a new, powerful Titan that was previously unknown. This Titan might have a vendetta against Percy specifically, seeing him as a major threat to their plans. Maybe they manage to kill Percy, but his rebirth sets in motion a series of events that will lead to their ultimate downfall.
A powerful demigod who has been corrupted by the idea of primordial power could be the main antagonist. They might believe that by allying with a primordial or obtaining their power, they can become greater than the gods. This demigod would then oppose Percy, who stands for the protection of the current order.
An ancient and forgotten god who has been awakened. This god could be angry at the modern demigods for ignoring the old ways and decides to send assassins after Percy as a warning to the rest. They might want to bring back the old order where gods were feared and worshiped more and see Percy as a symbol of the new, more independent demigods.
Perhaps an ancient and dark deity who has been awakened due to some event related to Percy's exile. This deity wants to bring chaos to the world of gods and demigods, and Percy, even in exile, is the only one who can stop it. The deity would use all kinds of dark magic and minions to oppose Percy and his friends.
A new and powerful Titan could be the main antagonist. This Titan could be jealous of Percy's immortality and see it as something that should belong to Titans instead. He could gather a new army of monsters and try to overthrow the Olympian gods once again, with Percy being the biggest obstacle in his way.
A powerful nature - hating Titan who wants to plunge the world into eternal winter could be a great antagonist. He would be directly opposed to Demeter's power over the seasons and crops.
It could be a powerful demigod who was once rejected by the Camp Half - Blood. This demigod, filled with resentment, forms a mafia - like group to seek revenge on those who he believes wronged him. He uses his powers, which could be something like controlling shadows, to create an air of mystery and fear around his mafia operations.
The main antagonist could be a primordial being that has been awakened. It sees the phoenix as a threat to its existence because the phoenix represents rebirth and renewal, which goes against the primordial being's nature of chaos and destruction. So, it tries to destroy the phoenix and Percy has to protect it, along with his friends, using all their skills and the unique powers they possess.
Maybe a rogue demigod who blames Percy for something and wants to make his exile permanent. This demigod could have some dark powers or be in league with some evil forces. They would constantly try to thwart Percy's attempts to return or find a way to clear his name.
Maybe an ancient sea demon that has possessed a pirate captain. This possessed captain is now leading his crew to cause chaos everywhere. They are attacking other pirate ships and even some demigod - related places. Percy has to find a way to exorcise the demon from the captain and stop the crew's rampage. The demon is very cunning and uses the pirate's knowledge of the sea to its advantage.