Maybe Sakura is being controlled by some dark force and is about to harm Naruto, so Gaara steps in to save him.
It could be that Sakura has a misunderstanding and is attacking Naruto in anger. Gaara, who has become Naruto's friend, doesn't want Naruto to get hurt and thus saves him. For example, Sakura might think Naruto has done something wrong to Sasuke, but in fact, it's a miscommunication. Gaara, knowing Naruto's true intentions, decides to protect him.
He could use his sand powers to create a barrier between Naruto and Sakura.
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 many Sasuke - Sakura - Gaara fanfictions, Sasuke saving Sakura from Gaara can be a really exciting plot. It often shows Sasuke's strength and his hidden feelings for Sakura. Maybe he uses his Sharingan to outwit Gaara's sand attacks and rescue Sakura just in time.
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.
One common theme is the display of Sasuke's heroism. He is often depicted as the strong and capable ninja who can overcome Gaara's power to save Sakura.
Well, a plot twist might be that Naruto actually gets captured by the Akatsuki while trying to save Gaara. Then, Gaara, in his weakened state, has to find a way to save Naruto instead. This would completely change the dynamic of the story. Or, it could be that the Akatsuki's real target isn't Gaara at all, but Naruto, and they use Gaara as bait. So when Naruto arrives to save Gaara, he walks right into their trap, but then uses his wits and new jutsu to turn the tables on the Akatsuki.
One common theme is friendship. Gaara and Sakura, who come from different villages, form a bond through the act of saving. It shows that even characters with different backgrounds can be friends.
Gaara's unique sand abilities and his connection to the tailed beast within him can add a lot of depth to a fanfiction. Sakura could be curious about this part of him and through her curiosity, they bond. Sakura's medical ninjutsu skills are also something to consider. Maybe Gaara gets injured and she has to use her skills to heal him, which leads to a deeper emotional connection between them as they talk during the healing process.
One possible story could be that Sakura goes to the Sand Village for a medical mission while Gaara is Kazekage. They start to interact more, and Gaara is impressed by Sakura's strength and kindness. Eventually, they form a strong friendship that helps in strengthening the bond between the Leaf and Sand villages.
One popular 'gaara saves sakura fanfiction' might be 'The Desert's Rescue'. In this story, Gaara uses his sand powers to shield Sakura from a powerful enemy attack just in time. It shows his quick reflexes and his growing bond with Sakura.