It could be Issei. Maybe he becomes jealous of Natsu's power or popularity in DxD High School and decides to betray him for his own gain.
It could be Gray. Although they are friends most of the time, in a fanfiction, there could be a plot twist where Gray's envy of Natsu's abilities gets the better of him, and he betrays Natsu. Maybe Gray thinks that by getting rid of Natsu, he can be the top mage in their guild.
One possible plot could be that Natsu, being in the DxD High School setting, is betrayed by someone he considered a close friend. Maybe this friend reveals Natsu's secrets to the enemies in the DxD world. As a result, Natsu has to face new challenges alone, all while trying to figure out how to deal with the betrayal and regain his trust in others.
He might also interact with Rias. Rias is a powerful devil and a leader. Sans could approach her with his laid - back attitude. She might be initially suspicious of him but later come to respect his abilities. They could have some strategic discussions about dealing with common enemies in the High School DxD world. And Sans could probably crack some jokes that would either amuse or baffle Rias.
He could have adventures in school competitions. For instance, if there's a magical sports event, Natsu's competitive spirit would surely make him strive to win. His dragon - slayer magic might give him an edge in something like a magical obstacle course race.
Akeno could also be a possibility. Her calm and sometimes mysterious nature might draw Kaido in. Their interactions could start with mutual respect due to their combat abilities and develop into something more romantic over time.
It could be Issei. Since he's always eager to become stronger and protect his friends, his encounter with the Annihilation Maker could lead to some really interesting storylines. He might be drawn to the Annihilation Maker's power and seek to learn from them to gain an edge in battles against the various threats in the High School DxD world.
A human with a special power that makes them a killer could also be a good choice. They could be an outcast in the human world because of their power, and then get drawn into the High School DxD world. Their journey from being a feared killer to finding a place among the supernatural beings would be an exciting story to tell.
It could be a powerful devil who sees the Ghost Rider as a threat to his plans in the school. Maybe this devil wants to take over the school or gain more power among the students, and the Ghost Rider's presence and his sense of justice stand in the way.
One way could be through the power system. The EMS (Eternal Mangekyou Sharingan) from Naruto could be a unique power that a character in the High School DxD world acquires. Maybe a transfer student from a hidden ninja village arrives at the high school and has to keep their EMS a secret while dealing with the devils and angels in the school. This could lead to some interesting battles and interactions as the powers of the EMS, like the ability to use powerful jutsus, contrast with the magic and abilities of the High School DxD characters.
One possible plot is that Gilgamesh views the High School DxD setting as beneath him at first. But as he gets to know the characters like Issei and Rias, he starts to see the value in their struggles. He could then use his vast resources and power to help them in their fight against stronger enemies, all while maintaining his haughty and kingly demeanor.