The main antagonist might be a new character, a powerful being that rules the realm where Percy is banished. This being could see Percy as a threat to his or her power and try to stop Percy from finding a way back.
A powerful sorcerer who also wants to claim the island for his own could be the main antagonist. He sees Percy as an obstacle to his plans and tries to eliminate him. The sorcerer might have control over some of the dangerous creatures on the island and use them to attack Percy.
The main antagonist might be an ancient and powerful being that has awakened. This being could see Percy and Annabeth as a potential threat to its plans of taking over the demigod world. So, it uses its influence to have them banished, thinking that without them, it would be easier to conquer. For example, a long - forgotten Titan who has found a way to break free from its prison.
It could be a rogue demigod who has a vendetta against Percy. This demigod might have spread the false rumors that led to Percy's banishment in the first place, and now he wants to make sure Percy never returns. He uses his own powers and manipulates other demigods and monsters to achieve his goal.
The gods themselves could be the main antagonists. Since they cursed Percy, they might be trying to keep him in a state of misery or use him for their own purposes.
Maybe an old and powerful monster that has long been trapped in Tartarus could be the main antagonist. It sees Percy as a threat or a source of entertainment, and it tries to stop him from finding a way out or from getting stronger.
Another possibility is a group of outlaws or rebels in the banished world who don't trust Percy because he's from another place. They might think he's been sent to spy on them or take over. So they would constantly try to get rid of him. They could be very resourceful and know the ins and outs of the new world better than Percy, which would make them tough opponents.
It could be an envious demigod who feels that Percy doesn't deserve his new position as a consort of the gods. This demigod might plot against Percy, trying to undermine his influence among the gods and the other demigods.
A group of rogue demigods who have turned against the gods and see Percy as a traitor for being so close to them. They form an alliance and try to stop Percy from fulfilling any quests or tasks given to him by the gods, and might even try to capture or kill him.
Set, the Egyptian god of chaos. He could be a great antagonist as he might see the combination of Greek and Egyptian powers in Percy and the other demigods as a threat to his own plans of spreading chaos. He could try to manipulate events to turn the two groups against each other.
The main antagonist could be one of the major gods who cursed Percy. For example, Zeus might be angry with Percy for some reason and decide to curse him. Zeus would then use his power to send all kinds of obstacles and enemies Percy's way. He could manipulate the weather to create storms that target Percy or send powerful monsters after him.