Sasuke could be a candidate. Given their complex relationship, Sasuke might find a way to give Naruto a new arm as a way to atone for their past differences. He could have discovered some rare medical ninjutsu during his travels or come across a powerful artifact that he uses to create a new arm for Naruto.
Maybe Orochimaru. Despite being a villain in the past, he is a master of forbidden jutsus and experiments. He could see Naruto as an interesting subject and give him a new arm with some dark powers, which Naruto would then have to learn to control for the greater good.
Well, one possibility could be that Naruto gets a new arm with some special abilities. Maybe it was given to him by a powerful ally or he discovers an ancient artifact that attaches to him as a new arm. This new arm could have powers like enhanced strength for his ninja techniques or the ability to sense danger more acutely.
Well, perhaps the new arm comes from some kind of ancient and mysterious source. It could be an arm that was once part of a powerful ninja from the past. This new arm could have a mind of its own, at first causing Naruto some trouble as he tries to control it, but eventually they work in harmony and it gives Naruto an edge in battles against tough enemies.
Well, it could be that he got it as a gift from some super - advanced ninja technology group in the fanfiction world. Maybe they saw his need for an extra weapon or tool during battles and decided to equip him with a metal arm.
One special ability could be enhanced strength. The metal arm might be able to deliver much more powerful punches than his normal arm, allowing him to break through tough defenses more easily.
Naruto would need to train harder to make up for the lack of an arm. He could develop new jutsus or modify existing ones. Maybe he would start using more wind - based attacks that can be controlled with just one arm and his chakra control. Also, his friends might help him by creating prosthetics or assisting him in battles.
Maybe he was protecting someone in Wave. He's always the self - sacrificing type, so he could have put himself in harm's way to save a villager or a friend.
One possible fanfiction could be about Naruto's right arm gaining a new and mysterious power. Maybe it starts to glow with an unknown chakra, and he has to figure out how to control it without losing himself. It could be a power that has a connection to an ancient ninja clan's secret technique.
Well, in some fanfictions, he might get it from a skilled ninja prosthetics maker. This maker could be someone who specializes in creating artificial limbs for ninjas who have lost their arms in battle.