Yes, there are quite a few. You can start by looking on fanfiction websites like FanFiction.net or Archive of Our Own. Just search for the specific tag 'sakura is kakashi's sensei' and you'll find a variety of stories with different plotlines and interpretations.
In the fanfiction, Naruto's new sensei could be a mysterious figure who has ties to the Sage of Six Paths. This person might have been waiting for the right time to appear and train Naruto. They could possess knowledge about the origin of chakra and how to fully unlock Naruto's power. It could also be someone who was once an enemy but has now changed their ways and wants to use their skills to train Naruto for the greater good of the ninja world.
There's a chance that Naruto's new sensei could be a self - taught ninja who has developed their own unorthodox style. This person sees Naruto's ability to think outside the box and wants to refine that in him. They could introduce Naruto to a new way of looking at chakra control and combat strategies that are completely different from what he has been taught so far.
Naruto's teaching style would likely be more hands - on compared to Kakashi. He would probably jump right into showing his students how to do a jutsu instead of making them figure it out mostly on their own like Kakashi did. Naruto has always been about hard work and determination, so he'd push his students to keep practicing until they get it right.
One plot idea could be that Sakura discovers a new side of her chakra control under Kakashi's teaching. For example, he might teach her how to use her chakra more efficiently in combat, leading to her developing new fighting techniques.
I think Orochimaru would be the most unexpected sensei. Usually, he's seen as a villain, but in a fanfiction, if he were to train Naruto, it would be extremely unexpected. He has a vast knowledge of jutsu, especially forbidden ones. He could teach Naruto some very powerful and unique abilities, but at the same time, Naruto would have to deal with Orochimaru's morally ambiguous nature.
He could have adventures in the Forest of Death. Anko has experience there, and she could take Naruto on more dangerous and secretive missions within that area. Naruto would learn how to better handle the perils of that forest.
In this fanfiction concept, it could lead to a really interesting dynamic. Jiraiya is a powerful and eccentric ninja. He could teach Naruto some really unique jutsu, like more advanced forms of Rasengan. And their relationship would be filled with Jiraiya's boisterous personality clashing and also complementing Naruto's determination.
In fanfiction, Naruto as a sensei often has a very unique dynamic with his genin team. He might teach them his own unorthodox ninja techniques, like his signature Rasengan. His experiences as a former underdog also shape how he trains his students, emphasizing perseverance and the power of friendship.
Yes, there are many Naruto fanfics out there. You can start by checking fanfic platforms like FanFiction.net or Archive of Our Own. Just search for 'hinata sensei' in the Naruto section and you'll likely find some interesting ones.