There could be an ancient primordial being that has been locked away for eons but is now awakened. This being believes that the Fates have been too strict in their control of the universe and wants to break free from the chains of fate. Percy, as the God of Fates, has to stop this being from causing total destruction.
A group of powerful and corrupted demigods could also serve as antagonists. They might have been promised great power by some dark force if they can disrupt the work of the Fates. So they set out to target Percy and try to stop him from fulfilling his role as the God of Fates.
Perhaps some of the older, more traditional gods could be antagonists. They might see Percy as a threat because he's now the God of Dinosaurs and they fear the power he could gain from controlling these ancient and powerful creatures. For example, Zeus might be worried that Percy's new role could disrupt the existing power balance among the gods.
The Titans could be the main antagonists. They might want to use the powerful weapons Percy is associated with to regain their power and overthrow the Olympians.
The Titans could still be antagonists. Even though they were mostly defeated in the original series, some of them might have found a way to use the power of the night to their advantage. For example, Kronos could have some remnant of his power that is now tied to the night and he wants to use Percy, as the God of Night, to regain his full strength.
The main antagonists could be the Titans who are still bitter about their defeat and want to disrupt the new balance that Percy is trying to create. They might see Percy as a threat to their plans of regaining power. Another group could be some rogue demigods who have been corrupted by power and don't want Percy to enforce balance as it would limit their own abilities to do as they please.
The Titans could be the main antagonists. They might see Percy as a threat to their plans of regaining power. Since Percy has the power of the stars, they could try to steal his powers or stop him from using them to protect the world.
The Titans related to chaos and destruction of nature could be great antagonists. For example, Cronus might want to use Percy's newfound power as the God of Nature to further his own dark plans.
Some ancient and powerful monsters could be antagonists. Since Percy is now connected to the Fates, any disruption in the natural order might attract these monsters. They could see the situation as a chance to gain power or revenge. For instance, a powerful Titan who was once imprisoned might see Percy's new status as a way to get back at the gods by attacking him.
A group of ancient spirits of chaos that have been awakened by the imbalance in natural disasters could be the antagonists. They thrive on destruction and see Percy as a threat to their plans of creating total chaos. They would constantly try to undermine Percy's efforts to control and prevent disasters, and they might possess other powerful beings to fight against him.
Obviously, the God of Death could be a main antagonist if he has some malicious plan. He might be trying to tip the balance of life and death in his favor, causing chaos in the mortal and demigod worlds.
The Titans could be great antagonists. They might see Percy as a threat to their power if he becomes the God of Elements. Kronos, for example, could try to steal Percy's newfound elemental powers to regain his full strength and take over the world again.