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.
Well, in some fanfictions, the plot might involve Percy and Annabeth getting married and having to deal with the challenges of family life while still being demigods. Their children could potentially have unique powers that draw the attention of both the gods and new threats. Or perhaps there's a plot where Percy has to go on a solo quest to a previously unexplored part of the mythological world, like a hidden realm of a minor god that holds a powerful artifact which, if in the wrong hands, could destroy the balance between the mortal and divine worlds.
It could be that the fanfiction focuses on the relationships between the different camps. For instance, Camp Half - Blood and Camp Jupiter might have some sort of competition or joint mission. Percy could be caught in the middle of a power struggle between different groups of demigods who have different ideas about how to handle the post - Heroes of Olympus situation. Maybe some demigods want to isolate themselves from the gods completely, while others want to strengthen the bond. Percy would have to navigate these complex relationships while also dealing with any external threats.