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.
One reason is their friendship. Naruto was one of the first people to see Gaara as a person, not a monster. So, Gaara would feel indebted to Naruto and be willing to risk his life. Another reason could be for the sake of the ninja world. Naruto is often seen as a key figure in maintaining peace, and Gaara, as a responsible leader, would understand the importance of saving him.
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.
For Naruto, he could develop a deeper understanding of the pain that Gaara has been through. This might make him more empathetic towards others who seem hostile at first. He might also learn new combat techniques from observing Gaara's use of sand in the heat of the Chunin Exams battles.
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.