He could create a jutsu that allows him to teleport short distances. Given his quick thinking and need for mobility in battles, a short - range teleportation jutsu would be very useful. It could be like a mini - version of Kamui but powered by his own chakra.
Naruto might be initially excited. He's always eager to learn new and powerful jutsu, and the Chidori is a very cool and strong one. He probably can't wait to start training and show off to his friends once he masters it.
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.
They could study ancient scrolls. In the Naruto world, there are often hidden scrolls with powerful jutsu. A character might stumble upon one that has the secrets of a new space - time jutsu. By deciphering the symbols and practicing the techniques described, they could develop the new jutsu.
The most exciting part is seeing new powers. For example, when Naruto gets a new jutsu, it could be something that completely changes the way he fights. It's like getting a new superpower.
There could be a jutsu that allows for instant teleportation across long distances. This jutsu might be a new discovery in the fanfiction world, perhaps created by a character who has been experimenting with space - time ninjutsu. They might use it to quickly get in and out of battles or reach far - off places in a blink.
If Naruto creates a very powerful and dangerous jutsu, some characters might be afraid of him. For example, the villagers who were once suspicious of his Nine - Tails power could again start to fear him. However, his close friends like Sasuke and Sakura would likely trust him and help him control and master the new jutsu.
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.
I'm not sure specifically as I haven't read that particular fanfiction. But generally, a 'Sasuke Oiroke no Jutsu' in fanfiction might involve Sasuke in some sort of comical or unique situation related to the Oiroke no Jutsu, which is the Sexy Jutsu in the Naruto universe. However, without reading it, it's hard to say more precisely.