Another possibility is that he works at the Ministry of Magic. Given his status as the Boy Who Lived, he might be given some special tasks or a regular job in a department. For example, he could be in the Auror department, learning from the Aurors and doing some basic tasks like filing reports or helping with the research on dark wizards.
He could work at Weasleys' Wizard Wheezes. He has a good relationship with the Weasley family, and it would be a fun place for him to work, helping with inventing and selling all kinds of magical pranks and toys.
Maybe he would work at Hogwarts. There are always things to do around the school during summer, like helping with the maintenance of the castle or taking care of the magical creatures in the Forbidden Forest under the guidance of Hagrid. This would give him a chance to be closer to the place he loves and also learn more about Hogwarts.
He could work at Flourish and Blotts. He's very knowledgeable about magic, so he could help customers find the right books. It would be a great job for him as he loves to read and study magic. He could also recommend books to young witches and wizards starting their magical education.
Hagrid could be a great help. He has a lot of connections in the wizarding world, especially with those related to magical creatures. He might introduce Harry to someone who needs help with taking care of or studying magical beasts, and thus get Harry a job in that area.
Well, he might work at Weasleys' Wizard Wheezes. He could help George and Ron with inventing new products and dealing with customers. It would be full of magical mishaps and lots of fun.
He could meet other young wizards and witches who are also working summer jobs. Maybe some from other wizarding schools.
Perhaps Harry gets a job as a magical tutor for some young wizards. The story could develop as he tries to teach them the things he's learned over the years. He'd face challenges like dealing with difficult students or trying to teach advanced magic to those who are not ready. His experiences at Hogwarts would come in handy, but he'd also have to learn new teaching methods.
Well, he could work at Hogwarts during the summer for a change. Maybe he's helping Hagrid with the care of magical creatures. He would get to interact with new and dangerous beasts, and at the same time, he might learn some new spells to keep them in check from other professors.
Obviously Harry would be one of the main characters. And Hermione might also be involved, perhaps she helps Harry get the job or gives him advice on how to do it well.
In a 'Harry Potter Summer Training' fanfiction, perhaps the training is organized by some of the older students who have graduated but still want to help. They could be teaching the younger students advanced dueling techniques. Harry might discover a new aspect of his magic during this training, something that has been dormant until now. For example, he could have an affinity for a type of magic that is rare, like time - related magic. The story could then revolve around him exploring this new power under the guidance of the older students.
In this fanfic, Harry might get a job as an Auror. He would be involved in solving magical crimes, going on dangerous missions, and working with his old friends to keep the wizarding world safe.
Dumbledore could be the instructor. He might have a special training program in mind for the students. He could teach them about the deeper mysteries of magic, like the secrets of the Hallows or the true nature of the Deathly Hallows. His wisdom and experience would make him an excellent teacher for the students during the summer training.