Perhaps a wizard with the power of illusions. This character could create all sorts of challenges for Natsu and the rest of Fairy Tail. Natsu would have to figure out how to see through the illusions and defeat this new adversary. Additionally, a character with a cursed magic that Natsu tries to help break the curse of would make for an interesting addition.
A character from a different guild who is on the run from some dark forces. Natsu could offer protection and in the process, this character could introduce new fighting styles and magic types to Fairy Tail. Also, a magical creature that can talk and has the power to sense hidden magic could be added. Natsu could befriend this creature and it could help him in his quests.
A young dragon slayer from a far - off land who has a unique magic related to the elements that haven't been seen in Fairy Tail before. Maybe his magic is connected to some aspect of the Dragon Cry.
There could be new characters introduced, like a wandering mage who also has a troubled past. This mage could understand Natsu's feelings of abandonment and they could become friends. Also, a character from a different guild that has always admired Natsu from afar might reach out to him.
Obviously, Natsu is a very popular character as it's in the title. He is often the center of many fanfictions. Lucy is also quite popular as she has a close relationship with Natsu in the original series. Their dynamic often plays a big part in fanfictions.
There could be a mysterious old wizard who takes Natsu under his wing when he leaves Fairy Tail. This wizard might have knowledge of ancient magics that Natsu is eager to learn.
In some fanfictions, Natsu as the 1st master of Fairy Tail might be depicted as a powerful and visionary leader. He could be shown as someone who laid the foundation for the guild's values of friendship and strength.
Well, they could have an interaction where Natsu accidentally sets off Juvia's temper. Maybe Natsu accidentally melts some of Juvia's precious water - made items. Juvia gets mad, but Natsu's cluelessness about how much he's upset her is kind of endearing. Eventually, Juvia forgives him when she sees how he was just being his usual, careless self.
Maybe an old acquaintance from Natsu's past that we haven't seen much in the original Fairy Tail story. This person could be a powerful but reclusive mage who decides to help Natsu out of respect for his father or some past debt. They could offer Natsu shelter and train him in new forms of magic to help him face the challenges during his exile.
Natsu could bring a more fiery and passionate leadership style. He'd probably be more action - oriented than the previous masters. For example, if there's a conflict with another guild, he'd be the first one to charge into battle, leading by example.
There could be a young orphan boy who lives in the attic of the Fairy Tail hotel. He has a natural ability to sense magic but doesn't know how to control it yet. The Fairy Tail members take him under their wing and try to help him develop his powers while also learning more about the hotel's history from him.
An American wizard detective. He could be investigating strange magical happenings in the wizarding world of America. The Potter character could cross paths with him and end up teaming up to solve a big case.