It could be Dumbledore. Even if he's dead in the original story, in fanfiction, anything is possible. He might have left behind some kind of magic that allows him to train Harry from beyond the grave, or he could have faked his death to take Harry to a secret location for training.
Perhaps Sirius Black. If he somehow survived in the fanfiction world, he would be a great candidate to train Harry. He has a lot of knowledge about the dark side of the wizarding world, having been in Azkaban and being a member of the Order of the Phoenix. He could teach Harry how to fight against dark wizards and how to be more street - smart in the wizarding world.
Well, in such a fanfiction, Harry might disappear to train in some hidden place, away from the prying eyes at Hogwarts. Maybe he goes to a secret location with a powerful wizard who teaches him advanced magic that he couldn't learn at school. This could include dark magic defenses or ancient spells.
There's a chance it could be a powerful house - elf. House - elves are known for their own brand of magic, and one particularly rebellious or enlightened house - elf could decide to train Harry in magic that is more about stealth and quick - thinking. After all, house - elves have to be very sneaky to avoid detection by their masters most of the time, and this kind of skill could be very useful for Harry in his battles against Voldemort.
Maybe it's a former Death Eater who has seen the error of his ways. He wants to atone for his past sins by training Harry to defeat Voldemort. He has inside knowledge of the dark side's tactics and uses this to make Harry a more formidable opponent.
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.
I think it could be Neville Longbottom. Neville has grown into a strong and confident wizard. He could have discovered boxing as a form of self - defense and then decided to teach Harry. Neville would bring his own unique perspective, having been bullied in the past. He'd train Harry to be both strong and fair in the boxing ring, emphasizing the importance of honor and respect in combat.
Sirius Black could be a trainer. Sirius, being Harry's godfather, would be highly motivated to train Harry. He could use the time - turner to go back to a time when he was at his peak in terms of combat skills and pass on his knowledge to Harry, especially in the areas of dark - wizard fighting and survival skills.
Voldemort could be the antagonist. Even if he was defeated in the original story, there could be a scenario where some remnant of his dark magic causes Harry and Hermione to disappear. Maybe he had a secret plan that was set to activate after his death and it involved taking them out of the picture.
It could be a new dark wizard who has been secretly plotting in the shadows. This wizard might be jealous of Harry's fame and power, and decides to make him disappear so that he can rise to power unopposed. He could have a group of followers who are experts in dark magic and are able to carry out his plan to make Harry vanish.
It could be Hagrid. He has a lot of strength himself and might know some basic principles of building muscle. He could guide Harry on how to lift the heavy weights, using his own brute strength as an example.
One possibility in this fanfiction is that Naruto's training with the Kyuubi helps him to better understand the nature of chakra itself. He could discover new ways to combine his own chakra with that of the Kyuubi, creating a unique and extremely powerful form of energy. This new form of chakra could give him an edge in future battles against powerful enemies. Also, his time training might be filled with various challenges and trials set by the Kyuubi, which would test his resolve and determination, making him an even stronger ninja in the end.