A simple plot could be that Hinata gets injured while on a mission, and Naruto takes it upon himself to nurse her back to health. During this time, they have long conversations and get to know each other on a deeper level, leading to the start of their romantic relationship.
In a fanfiction, perhaps there is a festival in the village. Naruto and Hinata both participate in different events. They accidentally keep running into each other throughout the day. They start to enjoy each other's company more and more, and by the end of the festival, they realize they have feelings for one another. They then start to date secretly at first, not wanting to make a big fuss in the village until they are sure of their relationship.
In this fanfiction, perhaps Hinata and Naruto are living together and learning more about each other on a deeper level. Hinata could be teaching Naruto some of the traditional Hyuga clan techniques, while Naruto shows Hinata some of his unique jutsu. Their living situation might also involve a lot of visits from their friends like Sakura and Sasuke, creating some really fun and heart - warming group dynamics.
It could also be a misunderstanding. Hinata might be framed as a traitor. Some false evidence could be planted that makes Naruto and his friends believe she has betrayed them. This would lead to a lot of drama and conflict in the fanfiction as Naruto struggles with whether to believe Hinata or the evidence against her.
The plot could involve Naruto protecting Hinata from the Hyuga clan's strict traditions. Since he's not bound by those traditions as her brother, he could fight against the elders who want to keep Hinata in a subservient role.
It could be about Naruto and Hinata going on a secret adventure together. Maybe they discover a hidden place in Konoha that no one else knows about and have to protect it from some sort of threat.
In a 'Naruto and Hinata reborn fanfiction', perhaps they are reborn with enhanced abilities. They might be reborn into a world where ninjutsu works differently. Naruto could be more in touch with his Uzumaki heritage from the start, and Hinata might have a new form of Byakugan. They would have to learn how to use these new powers together, and also navigate their relationship, which may be different from their past life due to different circumstances.
One possible plot could be that the Joker discovers a way to travel between universes and ends up in the Naruto world. He decides to target Konoha because it seems like a place full of order that he wants to disrupt. Naruto and Hinata notice the strange new presence in the village. They initially underestimate the Joker, but as he starts causing mayhem, they realize they need to combine their skills to stop him.
One possibility could be that in the fanfiction, Naruto has realized Hinata's unwavering love and support over the years. So, he starts to obey her out of respect and love. For example, Hinata might suggest a new training method for Naruto, and he obeys without question because he trusts her judgment. It could also involve Hinata having a say in Naruto's decisions regarding the village, as she is also a respected ninja.
The plot could involve Naruto achieving a godlike state and Hinata being the one who grounds him. For example, Naruto might be tempted by the power he has and start to lose sight of his values. Hinata, with her pure heart, helps him remember who he really is. They could then team up to face a powerful enemy that only Naruto in his godlike form can defeat, with Hinata providing crucial support and intelligence.
It could start with a strange phenomenon in the ninja world. Naruto and Hinata are in the wrong place at the wrong time and get caught up in it. As they become Hanyou, they discover that they can now communicate with certain spirits or demons. This new ability leads them to an ancient prophecy. They then have to figure out what the prophecy means and how it relates to their new forms. Their relationship also deepens as they rely on each other more in this new and dangerous situation.
One possible plot could be that Hinata accidentally stumbles upon Naruto's memories during a mission. Maybe they are in a strange place where memories are made visible, and Hinata starts to understand Naruto on a much deeper level. She sees his lonely childhood, his determination to be recognized, and his dreams for the future. This newfound understanding could strengthen their relationship and make Hinata more determined to support Naruto in his goals.