It could be Dumbledore, even if he's passed away. His portrait or some kind of magical remnant of him might still be able to guide Harry in learning new magic.
Maybe Hermione could be his mentor in this fanfic. She's always been very studious and knowledgeable about magic. She could share some of her research findings with Harry and help him master new spells.
It could be an older relative who was thought to be dead but actually has been living in seclusion, waiting for the right time to teach Harry about their family magic. This relative might have a vast knowledge of the family's magical traditions and spells.
Snape is a likely candidate. He is a skilled legilimens in the original series, and his relationship with Harry is already complex. Teaching Harry legilimency could be a way for Snape to either help or hinder Harry, depending on his motives.
It could be a powerful wizard from Asia who has long studied both magic and kung fu. This wizard has decided to pass on his knowledge to Harry Potter, seeing his potential.
Maybe a mysterious traveler from a far - off land. This traveler has mastered many unique jutsus including Dust Release. He crosses paths with Naruto during one of Naruto's solo adventures and takes him under his wing after seeing Naruto's eagerness to learn new techniques.
It could be Kakashi. Even though in the original story he doesn't teach Naruto the Rasengan, in a fanfic he might have some hidden knowledge about the technique. Maybe he was secretly studying it himself and saw Naruto's eagerness to learn new jutsu, so he decided to share his knowledge and help Naruto learn the Rasengan earlier.
Well, he might discover a long - lost spell. Maybe it's a spell that can make inanimate objects come to life and help him in his daily tasks at Hogwarts.
Obviously, Harry Potter is one of the main characters as it's about him learning magic. He is the central figure around which the story revolves.
Well, it could be that Harry has an encounter with an Egyptian wizard who decides to teach him their unique brand of magic. This magic might involve things like controlling the sands or communicating with mummies. Through his learning, he gains new powers and uses them to face his enemies in a different way than before.
Obviously, Harry would be one of the main characters. Since it's about him learning family magic.
A traveling nen master could be Naruto's mentor. This master could be on a journey to spread the knowledge of nen. He crosses paths with Naruto and decides to teach him. The master might have a strict teaching style, pushing Naruto to his limits, but also guiding him carefully through the complex world of nen.