He might learn Orochimaru's signature snake - related jutsu, like the Hidden Shadow Snake Hands. This jutsu allows the user to summon snakes from their sleeves or other hiding places to attack opponents.
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.
The apprentice could learn unique jutsu from Orochimaru. Since Orochimaru is known for his forbidden jutsu, the apprentice might gain an edge in combat but also face the danger of being corrupted by the power. They could then use these skills in battles against common enemies. And, in the process, they might try to redeem Orochimaru in some way, like showing him that there is a better path than his thirst for power.
He could create a jutsu like 'Blood Clone Jutsu'. Using Alucard's ability to manipulate blood, Naruto could create clones made of blood that have the same strength and abilities as him. These clones would be more durable than his regular shadow clones and could even explode on contact, causing damage with the blood splatter.
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 would likely become more secretive. Since Orochimaru is a very private and often devious character, Naruto might pick up some of those traits. He would probably keep things from his friends more often.
One possible new jutsu could be a healing jutsu using Quincy powers. Quincy have a connection to spiritual energy which could potentially be used for healing. Naruto, with his big heart and desire to protect, would surely find a way to use this to heal his friends or even himself during battle. He could also create a jutsu that imbues his shadow clones with Quincy powers, making them more effective in combat and able to perform tasks that normal shadow clones couldn't.
It could be a jutsu that manipulates life and death. Naruto has always been about protecting life, but this jutsu might give him the power to bring the dead back to life. However, this would go against the natural order of things in the Naruto universe.
She could teach him a genjutsu - based jutsu. For instance, a genjutsu that makes the opponent see multiple copies of Naruto, confusing them about which one is real. This would be useful in the Chunin Exams as it can give Naruto an edge in combat.
He could create an 'Explosive Rasengan'. By infusing the explosive properties of Deidara's bloodline into his Rasengan, it would be a jutsu that not only has the rotational force of the Rasengan but also the explosive power of Deidara's clay. It would be extremely powerful and could cause massive destruction.
Naruto's character would likely be darker. Orochimaru is known for his unethical experiments and thirst for power. Naruto, under his tutelage, might be more focused on individual strength rather than the bonds he values in the original series. He could become more secretive and less trusting of others.