Well, the characters might face new threats that emerged after the giant war. For example, some leftover magical creatures that were once under the giants' control could now be causing chaos. Also, they could have to deal with political unrest within the Olympian world as different gods vie for power in the post - war situation. There could be new quests to retrieve powerful artifacts that were lost during the chaos of the giant war. And of course, there could be new relationships forming among the heroes, both romantic and platonic, which would add more depth to the story.
I think Nico di Angelo could also be a central character. He has his own unique powers and backstory, and after the giant war, he might be involved in some of the darker or more mysterious aspects of the post - war world, like dealing with any remnants of the Underworld's connection to the giants' plans.
One interesting storyline could be about the heroes trying to rebuild their lives and the relationships that were strained during the war. For example, Percy and Annabeth might face new challenges in their relationship as they adapt to a post - war world.
Annabeth Chase would also be a main character. Her intelligence and strategic skills would be important in the rebuilding efforts. And of course, her relationship with Percy is a major aspect of the story.
A new main antagonist could be a forgotten or banished god. There are many minor gods in Greek and Roman mythology that haven't been explored much. One of them could be angry at the demigods for getting all the attention and decide to cause chaos. For example, a god of misfortune who decides to curse the demigods with a series of bad luck that leads to dangerous situations.
He could have adventures that involve mentoring the younger demigods. Since he's an adult, he has more experience. He might lead them in more complex quests, like exploring uncharted parts of the mythological world that are too dangerous for the younger ones alone.
Perhaps some of the demigods from other camps that he didn't interact much with before could become his new allies. They might see his leadership during the war and want to be part of his group, to learn from him and fight alongside him in any future conflicts.
They might travel the wizarding world together, exploring new magical creatures and hidden places. For example, they could go to the far - flung corners of the Forbidden Forest where few wizards have ever ventured.
Maybe the characters start to rebuild their lives. For example, they might focus on restoring the damaged places and re - establishing relationships that were strained during the war.
One possible plot development could be Percy and his friends facing a new, even more powerful enemy. Maybe an ancient primordial being that was previously sealed away has been awakened. For example, a new Titan or a primordial chaos entity. Another development could be Percy exploring his new powers or abilities that he might have gained after the events of Heroes of Olympus. He could be training other demigods as well, passing on his knowledge and skills.
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.