There's a chance it could be a spirit. In the Naruto universe, there are many spiritual entities. A spirit might appear to Naruto and offer to teach him hypnosis in exchange for Naruto helping it with some unfinished business. This would add an interesting spiritual aspect to the fanfiction.
It could be a wandering sage. These sages are often full of strange and powerful knowledge. They might see potential in Naruto and decide to teach him hypnosis as a way to expand his combat skills.
Well, one possibility is that Naruto learns hypnosis from a mysterious ninja. This new skill helps him in battles by confusing his opponents. He could use it to make enemies see illusions of multiple Narutos, giving him an edge in combat.
A powerful and corrupted sage could be the villain. He has delved too deep into forbidden arts and mastered hypnosis among other dark techniques. He views Naruto as a potential obstacle to his goal of spreading chaos and Mei as a valuable asset to be controlled. He uses hypnosis to try and manipulate them into doing his bidding. This sage could have a backstory of being shunned by the ninja world for his unethical practices, which has led him to seek revenge and power through any means necessary, including using hypnosis on Naruto and Mei.
It could be an old hermit. You know, those wise old guys who live in the mountains and have been guarding ancient ninja secrets. He sees potential in Naruto and decides to pass on the lost taijutsu to him.
Well, one possible plot could be that an enemy uses hypnosis on Mei and Naruto has to break the spell. He might have to go on a journey to find a rare antidote or learn a special jutsu to counter the hypnosis.
In a fanfiction, it could be that Tenten herself is the one who hypnotizes Naruto, but for a good reason. Maybe she wants to help Naruto overcome some inner fears or traumas. She uses her unique form of hypnosis that she has learned from an ancient ninja scroll. Under the hypnosis, Naruto relives some of his past experiences in a more controlled way and is able to face his fears. Tenten then guides him through the process, and when Naruto wakes up from the hypnosis, he is stronger both mentally and emotionally.
Well, it could be about Naruto being hypnotized by Mikoto into believing he has certain powers or a different identity. Maybe she hypnotizes him to help him overcome some fears or traumas.
In a more creative fanfic, an ancient ninja who was the originator of the Chidori technique could appear. This ninja could be brought back to life through some sort of magic or jutsu. He sees Naruto's pure heart and decides to pass on the Chidori knowledge to him, believing Naruto will use it for good.
Maybe an ancient sage in Naruto's own world who has long - been in seclusion. This sage has knowledge of different power systems beyond just chakra. He notices Naruto's pure heart and strong will and decides to pass on his knowledge of haki to Naruto, believing that Naruto can use it for the greater good of the ninja world.
Sasuke could be one of the people to teach Naruto new jutsus. They have a friendly rivalry and Sasuke has some unique jutsus like his Rinnegan - related abilities. He could teach Naruto some aspects of the Rinnegan's power, or at least how to counter it more effectively which could be considered a new 'jutsu' in a sense.
A traveling Muay Thai expert could teach Naruto. This person might be passing through the Ninja world and be impressed by Naruto's spunk. He decides to take Naruto under his wing and teach him the art of Muay Thai.