Perhaps Hinata's Kitsune heritage comes with a set of rules and traditions. Naruto, in order to be with Hinata, has to learn and respect these. This process of him learning about her Kitsune side and adapting to it can create a very special and unique development in their relationship. He could participate in Kitsune festivals with her or learn the significance of Kitsune symbols which are important to her family.
In a Kitsune Naruto x Sasuke fanfiction, their relationship might develop in a unique way if Naruto's kitsune form has a special connection to Sasuke's Sharingan. Maybe the kitsune's chakra can enhance the power of the Sharingan, but only when their emotions are in sync. So, they have to work on their emotional connection, which in turn deepens their relationship on a more personal level. They start to rely on each other not just in battle, but also in understanding and controlling these new powers.
For Naruto and Hinata, their relationship could develop in a unique way if Hinata starts teaching Naruto some of the more refined aspects of the Hyuga clan's techniques. This would create a new level of closeness as Naruto respects Hinata's skills. And with Tenten, she could be the one who arranges little 'get - togethers' for the three of them, which slowly builds a stronger bond between all of them.
The Kitsune aspect can make Naruto more mysterious and alluring to Hinata. His unique powers and form can be something that draws her in and makes her see him in a new light.
Perhaps they could be brought together through a shared love for gardening. Naruto, who has always been interested in growing things (as seen with his love for ramen ingredients), and Mebuki, who might have a beautiful garden at home. They start sharing gardening tips and gradually open up to each other about their dreams and fears, thus deepening their relationship.
Maybe they are both involved in a competition within the village, like a ninja - skills tournament. At first, they are rivals, but as they face different opponents, they start to respect each other's abilities. This mutual respect then turns into a strong bond as they help each other train and improve.
A very unique way would be if they get trapped in a time - loop together. They have to rely on each other to break free and in the process, they learn things about each other that they never knew before, leading to a deep and different kind of relationship.
Their relationship could be developed uniquely by having Kakashi become a more emotional mentor to the female Naruto. Instead of his usual calm exterior, he shows vulnerability in front of her, which makes her see him in a new light. This could lead to a deeper level of trust and friendship between them.
A really unique way to develop their relationship is to have them swap abilities for a short period. Naruto gets some of Kurama's fox - like abilities and Kurama gets some of Naruto's human abilities. This forces them to understand each other's perspectives in a whole new way. They have to learn how to use these new abilities and in the process, they become closer. Another aspect could be that they are both transported to a parallel dimension where they are the only ones who know each other. They have to rely solely on each other to survive and find a way back home, which would greatly enhance their relationship.
One way is to put them in a situation where they have to take care of a young orphan together. This shared responsibility would force them to communicate, cooperate, and rely on each other. Through this, they would see different sides of each other. Sai might show his nurturing side, which Fem Naruto has never seen before, and she would show her motherly - like instincts. This would create a new level of closeness between them that is different from their normal ninja - comrade relationship.
A unique way to develop their relationship could be through a time - travel plot. They could be sent back in time to when they were children. This would give them the chance to change some of the events that led to their strained relationship in the original timeline. They could also get to know each other all over again, but with the knowledge and experiences they have from the future, which would lead to a very different and more intimate relationship.