He could meet his future self. This encounter might be full of surprises as his future self could have different views and experiences. His future self might be more jaded or more powerful.
Percy may meet the descendants of his friends. For example, he could come across a young demigod who is the grandson of Annabeth. This new character might inherit some of Annabeth's wisdom and architectural skills, but also have unique abilities of their own.
One possible plot could be that Percy discovers a magical device that sends him to the future. There, he might find a world that has been drastically changed by the actions of the gods in his time. Maybe the demigod camps have evolved into something completely different, and he has to adapt to new rules and powers.
Percy might meet an old enemy who has somehow been resurrected or changed in the future. This enemy could be more powerful and have a new plan to take over the world or destroy the demigods. Or he could meet a group of time - traveling demigods from an even further future who are trying to fix something in Percy's future that has gone wrong.
He could meet other demigods from different regions. For example, a demigod from Scandinavia with powers related to ice.
He might encounter advanced technology that he has no idea how to use. For example, flying cars or holographic communication devices. It would be really funny to see him struggle with these new things at first.
Past Percy is likely to be more impulsive. He hasn't faced as many challenges yet and might act before thinking. Future Percy, on the other hand, would be more cautious and calculating, having learned from past experiences.
He could meet an old wizard who has been guarding the vault for centuries. This wizard could either be a friend or a foe, depending on Percy's actions.
He could meet his old teachers again. They might be surprised to see him back after his long absence.
Percy might run into his old friends' ancestors. This could create some really strange and exciting interactions. For instance, if he meets an ancestor of Annabeth, he could learn things about her family history that she doesn't even know.
He might meet alternate versions of his family members. Maybe a Percy from another universe whose mother is a powerful queen instead of a mortal.
He could meet some of the older campers who usually don't interact with the new arrivals right away. They might give him some special advice or warnings about the camp.