Harry Potter himself is surely important. He is the main character and the one going through the 'summer of change'.
Ron Weasley might be another important character. His loyalty to Harry could be tested or strengthened during this period of change. And his family, the Weasleys, could also be involved. Mrs. Weasley might offer some motherly advice or support to Harry during the summer, and the other Weasley siblings could be part of the adventures or changes that Harry experiences.
The important characters could also include some of the Hogwarts professors. They might be keeping an eye on Harry during the summer, or there could be a plot where one of them needs Harry's help. Even some of the minor characters from the original series, like Neville or Luna, could pop up and have an impact on Harry's summer. They could bring different perspectives or abilities that contribute to the overall theme of change in the fanfic.
It could also focus on some of the minor characters from the original series. For example, Neville could be a main character in this fanfic and his growth and change during the summer could be the main focus. Or Luna, with her unique perspective, could be in the center of all the happenings during that summer of change.
Harry Potter himself, of course. He has always been at the center of things in the wizarding world. His actions and decisions would likely have a great impact on any change that occurs.
In some fanfictions, Harry might change physically. He could have grown taller or more muscular from any summer training he did. For example, if he was secretly practicing Quidditch on his own, it could have affected his physique. Also, mentally he could have become more mature. Maybe he spent the summer reading advanced magic books and this broadened his understanding of magic, making him more confident and less impulsive in his actions.
Well, physically he could change too. Fanfic writers might describe him as growing taller or stronger during the summer break. Emotionally, he might deal with his past traumas better. For example, if he had nightmares about Voldemort, he could learn to overcome them, perhaps through some new magical techniques he discovers or with the help of his friends. This could make him more resilient and less haunted by his past, which is a significant change for his character.
Harry, Hermione and Ron are staples. But don't forget about Fred and George Weasley. They could be at the summer camp causing all sorts of mischief and coming up with new pranks. Seamus Finnigan might also be there, with his penchant for accidentally setting things on fire with his magic. And then there are the teachers. Hagrid could be at the summer camp, introducing the students to all sorts of magical creatures. Snape might be there too, though still as grumpy as ever, teaching potions or some other dark arts - related subject.
In many Harry Potter summer vacation fanfictions, Sirius Black is also a character that shows up. Given his relationship with Harry and his status as a wrongly - accused wizard. He could be involved in protecting Harry during the summer or helping him with some secrets about his family. Luna Lovegood might also be included, with her unique perspective on magic and the wizarding world, she could add an interesting element to the summer vacation stories.
Obviously, Harry Potter himself is crucial. Then there would be the other Slytherin students like Draco Malfoy. Their relationship could be very different in this fanfiction. Maybe they become allies instead of rivals. There could also be the Slytherin professors who play important roles in guiding Harry as the new 'king' of the house.
Obviously, Harry Potter is the central character. But in this fanfiction, 'life' could be personified as an important character too. It might be some sort of spirit or entity that has a big influence on Harry's upbringing.
In 'harry becomes lord potter at 7 fanfiction', Harry is the main character, but there could be other important characters too. Maybe there are some members of the Potter family's old allies who come forward to help Harry. For example, the Longbottoms could be important as they have a long - standing relationship with the Potters. And then there might be some antagonists, like the Malfoys, who could be envious or try to undermine Harry because of his new title.