Kakashi, as Naruto's former teacher, could also continue to teach him new jutsus. He has a vast knowledge of different jutsus from various elements. He could teach Naruto some new lightning - style jutsus, or some combination jutsus that combine different elements in a more efficient and powerful way.
Jiraiya could return in some form in the fanfiction and teach Naruto more sage jutsus. Jiraiya was a master of Sage Mode and there could be more to it that he didn't have time to teach Naruto before. Maybe some sage jutsus that are specific to the Mount Myōboku toads and can be used to enhance Naruto's existing abilities even further.
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.
He might learn a time - traveling jutsu. This would be really cool as it could allow him to go back and change certain events in the Naruto world, or gain knowledge from the past to use in the present battles.
He could potentially learn the Flying Thunder God Technique. It's a very powerful jutsu that Minato was famous for. Naruto's already fast with his Sage Mode and Nine - Tails Chakra, and this would make him even more formidable in battle.
If Naruto invented the 'Energy Absorption Jutsu', it could change the plot significantly. He could absorb the chakra or energy of his enemies, weakening them while strengthening himself. This would make him an even more formidable opponent and could potentially shorten battles, as he could quickly disable foes.
In fanfiction, Naruto learning the Vacuum Jutsu could be really cool. It might give him a new and powerful offensive technique. Maybe he'd learn it from an unexpected source, like an old hermit in a forgotten land. This could potentially change the power dynamics in battles he's in.
One jutsu he could invent is the 'Elemental Mimicry Jutsu'. With this, Naruto could temporarily take on the properties of any element he has encountered. For example, he could become as fluid as water to slip through attacks or as solid as earth to withstand powerful blows.
He could become even more powerful. The Vacuum Jutsu might allow him to defeat stronger enemies more easily.
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.
If he learned a healing jutsu, he would become more nurturing. He could use this jutsu not only to heal his friends in battle but also to help the villagers. His reputation would change from just a powerful fighter to also a healer, and he would be more respected in a different way.
Maybe Sasuke. Although they are rivals, they also have a deep bond. Sasuke might have come across a unique jutsu during his travels and decide to teach it to Naruto so that they can both become stronger and better protect their village.
Well, he might start with intense training sessions. Maybe he observes Kakashi closely for the Chidori, and for the Rasengan, he practices over and over again, gradually getting the hang of the chakra control required.