Maybe he'd discover some magical creatures native to the island. He could form an alliance with them, like how he befriended various magical beings at Hogwarts. He could also use the natural resources of the island along with his magic to build a shelter and find food. Since he's a wizard, he might even be able to magically purify water sources on the island.
Another possibility is that he starts to practice new forms of magic that he hadn't had the chance to explore before. He could be alone with his thoughts and memories, which might lead him to unlock some hidden power within himself. He could also have flashbacks to his time at Hogwarts and the lessons he learned there, which could help him survive on the island.
Harry would probably start by making a secure place to stay. With his magic, he could create a protective perimeter around his campsite to keep away any dangerous animals or magical creatures. He'd also have to deal with his own emotions. Being alone on an island might make him feel homesick at first, but his Gryffindor courage would help him persevere. And he might try to find a way to communicate with the outside world, perhaps by using his Patronus to send messages if he could figure out how to make it reach the right people.
They could start to build a community. For example, the stronger animals might help the weaker ones find food and shelter. Maybe the birds could use their beaks to gather twigs for building nests, and the monkeys could climb trees to get fruits for everyone.
In this fanfic, perhaps Harry could turn the island into a magical sanctuary for endangered magical creatures. He might build a school there for young witches and wizards who are overlooked by the mainstream magical education system.
Some animals might look for fresh water sources immediately. For example, they could follow the sound of running water or look for areas where the ground is damp. Also, they may start to explore the island to find suitable shelters like caves or thick bushes to protect themselves from predators and bad weather.
In some fanfictions, Harry Potter might discover a hidden magical object in the bathroom. For example, a secret passage could be revealed behind a mirror or a sink when he's in there alone, leading him to a new adventure or a place filled with ancient magic.
Well, Harry could get involved in some really off - the - wall pranks. Since he's bored, he might decide to play some elaborate tricks on his friends, like magically changing their voices during class.
In fanfiction, if Harry Potter disappears, it could lead to chaos at Hogwarts. His friends like Hermione and Ron would likely be on a desperate search for him. They might suspect the Dark forces at work again, and start investigating all the possible places where Harry could have been taken or hidden.
In fanfiction, Harry Potter could be wrongly accused of using dark magic in court. Maybe some false evidence is presented against him, like a planted dark magic item. And he has to fight to prove his innocence.
Well, it could be a meeting between Harry and some long - lost relative. Maybe a wizard from a far - off land who has a connection to his family. It could bring new revelations about his past and powers.
In fanfiction, the possibilities are endless. It could be that they go on an adventure to a previously unknown magical land or face a powerful dark wizard who was thought to be defeated.