One way is by making him a new member of the Hunt. He could bring his unique skills like sword fighting and water control to help the Hunt achieve their goals. Another way is that he could be a reluctant ally, initially not wanting to be involved but getting drawn in due to some common threat.
Well, Percy could be incorporated in multiple ways. Firstly, his connection to the gods could play a role. Maybe the Hunt is on a mission related to Poseidon, and Percy's knowledge of his father could be crucial. Secondly, his demigod powers could be used in the Hunt's adventures. For example, if they are in a forest and need to cross a large river, Percy can use his water - based powers to create a path. Also, his personality, being brave and resourceful, could inspire the members of the Hunt or cause some internal conflicts as his way of doing things might be different from theirs. He could also be a love interest for one of the Hunt members, which would add a whole new layer of drama to the fanfiction.
There are several possible ways. He could be a guide in the fanfiction. Since he has a lot of experience in the mythological world, he could lead the Hunt through dangerous terrains or help them understand complex mythological puzzles. His powers can also be a key factor. For instance, if there is a sea - related mystery or a need to communicate with sea creatures during the Hunt, Percy would be indispensable. Moreover, his backstory as a hero in his own right can be used to create parallels or contrasts with the Hunt's story. He might share his tales of fighting monsters with the Hunt members, which could either boost their morale or make them a bit envious of his achievements. And of course, his character arc within the fanfiction could be about learning to work within the Hunt's rules and values while still maintaining his own identity as a demigod.