They're similar in their tenacity. Naruto never gives up, no matter how tough the situation is. He keeps fighting against powerful enemies like Pain or Sasuke. Gaara is the same. He has faced numerous challenges, especially when dealing with the internal and external threats to his village. Despite his past traumas, he stands firm. Also, they both understand the pain of being an outcast, which makes them empathetic towards others who are suffering.
Well, Naruto could be depicted as being similar to Gaara in their inner strength. Gaara was always strong on the outside but had a fragile heart. Naruto, in this fanfiction, may share that same duality. Maybe he shows Gaara that having a strong will doesn't mean suppressing emotions. He could be the one to show Gaara that it's okay to let others in, since Naruto is always about making friends and bringing out the best in people.
At first, their relationship might be a bit guarded. Gaara, being used to isolation, might be hesitant to open up to Naruto. But as they face challenges together, like fighting a common enemy, they would start to respect each other's strength. Naruto's positive attitude would gradually break down Gaara's walls, and they would become friends.
Naruto would likely show Gaara that the village can be a place of acceptance. He could introduce Gaara to the villagers, starting with the kids. The kids' innocent acceptance of Gaara would be a big step in changing his view. For example, they could play games together in the village square.
Naruto would probably still be his enthusiastic and determined self, but with a new sense of responsibility as a Wizard Saint. He might be a bit more cautious in using his powers since they are now magical and could have greater consequences. Gaara, on the other hand, might become more open. The new role of Wizard Saint could give him more confidence and he could start to interact more with others in a positive way, rather than just being aloof.
Well, in many fanfictions, it might start with Gaara noticing Naruto's unique strength and unwavering spirit. Naruto's ability to reach out to others, even his enemies, could be very appealing to Gaara. Maybe during a joint mission, they have to rely on each other, and Gaara starts to see Naruto in a different light, gradually developing deeper feelings as they spend more time together.
Well, in many such fanfictions, Gaara might use his sand powers. He could sense Naruto is in danger through his connection to the sand or his own instincts. Then, he'd quickly move in, using his sand to shield Naruto from any attacks by the Akatsuki members, like blocking their jutsu with his powerful sand barriers.
In the fanfiction, Naruto might comfort Gaara by sharing his own experiences of being an outcast. He could tell Gaara about how he was shunned in the village at first because of the Nine - Tails inside him. Naruto would say that just like him, Gaara has the strength to rise above people's fear and hatred. He might put his hand on Gaara's shoulder and give him a reassuring look, saying that they are both jinchuriki and they can support each other.
In this fanfiction, Gaara's possessiveness could be demonstrated in different ways. Firstly, he might be possessive in terms of her time. He wants to spend as much time as possible with her. Secondly, he could be possessive about her emotions. He doesn't want her to be too friendly with other guys as he fears she might develop feelings for them. Also, he may be possessive about her safety, always being on guard and ready to fight off any threats to her.