Naruto would gain better combat awareness. Kurama's experience in battles can be passed on to Naruto. He'll be able to read his opponents better, know when to attack and when to defend. This will make him a more formidable opponent in combat situations.
Well, Kurama might train Naruto by teaching him how to better control and access chakra. Since Kurama has a vast amount of chakra, it could show Naruto unique ways to harness and use it. For example, it could guide Naruto in creating more powerful and complex jutsu by using their combined chakra in a more efficient way.
In this kind of fanfiction scenario, Naruto might gain some unique powers and skills. He could learn advanced chakra control techniques that are specific to the future version of Kurama's knowledge. Maybe he would also have a different perspective on his ninja way, as the future Kurama might have different insights based on events that haven't occurred in Naruto's time yet.
In fanfiction, if Naruto and Hinata were trained by Kurama, they would likely become extremely powerful. Naruto already has a connection with Kurama, and with Hinata by his side, Kurama could teach them new jutsu and ways to better control their chakra. Maybe they would develop unique combat styles that combine Naruto's brute force and Hinata's elegance, making them an unbeatable duo in the ninja world.
In such a fanfiction scenario, Naruto might gain some really unique powers. The Shinigami could teach him about different forms of spiritual energy which could enhance his already formidable chakra. Maybe he'd learn to manipulate souls or gain a new level of perception.
The plot could involve Kurama teaching Naruto how to use his own chakra more efficiently. Since Kurama is a powerful source of chakra, he can guide Naruto on how to tap into his inner strength. Maybe Naruto starts to show extraordinary abilities in front of the villagers even before the academy, which causes both fear and admiration. This early training could also lead to Naruto having a different attitude towards his studies at the academy as he already has some skills.
His character would become more mature. With the future Kurama's training, Naruto would face different challenges that force him to think and act more like an experienced ninja, rather than the impulsive one he used to be.
In this fanfiction, Naruto might gain some unique and deadly water - style techniques from Zabuza. Zabuza is a master of assassination and water - style jutsu. So Naruto could become more stealthy and proficient in close - combat water attacks. He may also learn about the darker side of the ninja world from Zabuza, which could make him more cynical or more understanding of the different kinds of shinobi out there.
He would probably become extremely powerful. The Grand Priest is an incredibly powerful being in the Dragon Ball universe. Naruto, with his already impressive ninja skills and determination, could gain new abilities like energy manipulation or enhanced speed and strength.
He might gain extremely powerful and unique abilities. The high priest could teach him ancient and secret techniques that are not known in the normal ninja world. This would likely make Naruto even more formidable in battles, and perhaps give him a deeper understanding of spiritual or otherworldly powers.