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.
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.
I'm not sure if there is such a specific fanfiction. Fanfiction can cover a wide range of very creative and sometimes out - of - the - ordinary ideas, but this one seems rather unusual. You might try searching on some large fanfiction websites to see if it exists.
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.
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.
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 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.