Well, the fanfiction could also explore how Naruto's personality is affected. Maybe he becomes more empathetic due to the influence of the female Kurama. He could start to view the world from a different perspective, not just as a ninja trying to protect his village, but also as someone who has a deeper connection to the spiritual and natural forces in the Naruto universe.
One possibility is that Naruto's relationship with Kurama would change significantly. Instead of the more adversarial or begrudging relationship he has in the original series, with a female Kurama as his trainer, it could be more nurturing. This might make Naruto more in tune with his inner self and his own power source, leading to faster growth as a ninja.
In this kind of fanfiction, Naruto might gain unique powers. Since Kurama is a powerful being, being trained by a female Kurama could lead to Naruto having a different combat style. He may learn more about chakra control in a new way. For example, he could develop a special jutsu that combines his own natural abilities with the knowledge imparted by the female Kurama.
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.
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 such a fanfiction, Naruto might gain unique and powerful abilities. Kurama could teach Naruto more efficient ways of using chakra, like advanced chakra control for his shadow clones. This could make Naruto's clones stronger and more versatile in combat.
Well, Naruto might gain new and powerful jutsu. Kurama could teach him some unique chakra control techniques that no one else in the village knows. This would make Naruto even more formidable in battle.
Another interesting plot might be that the female Kurama reveals to Naruto secrets about his family. Maybe there are hidden connections between his family and the origin of Kurama. This would add a whole new layer of mystery and depth to Naruto's character development.
Naruto would become more confident. With Kurama's training, he'd know he has more power and skills at his disposal, so he'd face challenges with less hesitation.
In such a fanfiction, Naruto might become extremely powerful at a young age. Kurama could teach him unique jutsu and survival skills. He would also likely have a very different view of the tailed beasts compared to canon Naruto.
There could be a time - travel fanfiction. Naruto, with the help of Kurama's power, accidentally travels back in time and meets a young Gaara. Naruto then tries to change Gaara's future for the better, using his knowledge from the future and the power of Kurama. This could create a whole new set of adventures and relationships between the three.