He could gain the power of manipulation. Gaster might give Naruto the ability to manipulate space or time on a small scale. Maybe he could create small portals or slow down time for a short period during combat.
Naruto might gain some really unique powers. For one, he could potentially get the power of enhanced knowledge. Gaster seems to be associated with a lot of mystery and knowledge in some fan theories. So Naruto could suddenly have insights into things he never knew before, like ancient jutsu or the secrets of the ninja world. Another power could be the ability to phase through objects. If Gaster has some form of intangible existence, he could pass this on to Naruto, allowing Naruto to dodge attacks more easily by phasing through them. He could also gain the power of energy projection, where he can send out strange, Gaster - like energy blasts that are different from his normal chakra - based attacks.
Well, Naruto might become more mysterious. Since Gaster is an unknown and rather enigmatic entity, Naruto could start having strange thoughts or powers that he doesn't fully understand at first. He might seem more withdrawn as he tries to figure out what's going on inside him, and his normal cheerful and straightforward personality could be clouded by the presence of Gaster.
He might gain some of Madara's Sharingan - related abilities. Maybe he could use some of the advanced genjutsu techniques that Madara was proficient in. Since Madara had strong chakra, Naruto could also potentially have an increase in his own chakra levels or a new way to manipulate chakra, like Madara's ability to control the Susanoo.
Naruto might be able to create cloud - based illusions. Just as he can create shadow clones, with the power of Cloud sealed in him, he could project illusions made of clouds to deceive his opponents. These illusions could be large - scale and very realistic, confusing enemies about his true location and intentions.
He might gain the ability to use his parents' chakra more directly. For example, if his father was good at a certain type of jutsu, Naruto could potentially access that more easily. Maybe some kind of enhanced speed or strength that was unique to his father.
In many such fanfictions, it could be a variety of deities. It might be an ancient and powerful god from Naruto's world's mythology that the story's author has chosen to insert. For example, it could be a god of elements like a super - powerful fire god, which could give Naruto even more control over his existing fire - based jutsu and new, more extreme abilities related to fire.
I'm not entirely sure if there is a specific fanfiction with exactly that premise. However, given the popularity of both Naruto and the concept of sealing powerful entities in Naruto's world, it's quite possible. Fanfiction writers love to experiment with combining different fictional elements, so it wouldn't be surprising if someone has written a story where Jenova is sealed in Naruto. You can try searching on popular fanfiction websites like Fanfiction.net or Archive of Our Own to find out for sure.
He might gain Minato's teleportation jutsu. It was one of Minato's signature moves, and with Minato sealed in him, Naruto could potentially access and learn this powerful technique.
One implication could be a significant power boost for Naruto. Since Kaguya was an extremely powerful being, having her sealed within him might give Naruto access to new levels of chakra and abilities. For example, he could potentially gain more control over space - time ninjutsu, which was Kaguya's specialty. This could make him even more formidable in battles against powerful foes.
Maybe it's an ice - dragon. This would be an interesting contrast to Naruto's usual warm - hearted personality. The ice - dragon's power could be used in creative ways in battles, like freezing opponents or creating ice - based defenses.
With his enemies, it would be a whole different story. They might be more cautious about attacking Naruto. Some might even try to find a way to use the god sealed in him for their own purposes. And Naruto's relationship with the hidden villages could also change. They might see him as a potential threat or a very valuable asset.