He could form a mentor - like relationship with some of the younger characters in High School DxD. His experience and power could help them grow. Also, he might have an uneasy alliance with the devils, as they could be interested in his power. Maybe a friendly rivalry with some of the more powerful angels.
He could form a friendly rivalry with Issei. Since Issei is all about power and his Boosted Gear, and Asta is super determined with his anti - magic sword, they could compete in terms of strength and growth. They might also learn from each other's combat styles.
If Naruto had Kyuubi's power in the High School DxD universe, things would be chaotic at first. His presence would be a shock to the different factions. The devils would likely try to either recruit him or eliminate him. But Naruto, with his strong will and Kyuubi's power, could form new alliances. He could teach the students at the school some of his ninja ways and in turn learn about the magic and powers in that world. His Kyuubi - enhanced abilities would make him a formidable opponent in the Rating Games.
Well, they could be involved in a school sports competition. Naruto would be all about the spirit of the game, while the Female Kyuubi might initially be reluctant but then get really into it to prove her strength. Or perhaps they are in a club together, like a mystery - solving club. They would use their unique skills, Naruto's ninja skills and the Kyuubi's intuition, to solve various strange events that happen around the school.
Well, the story could start with Naruto and Fem Kyuubi being transferred to the High School DxD school. Naruto might struggle to adapt to the different rules and social hierarchy there. The Fem Kyuubi, on the other hand, could use her charm and wits to navigate through the new environment. Their relationship could evolve as they face challenges together, like dealing with the various factions in the school.
There could be a storyline where Naruto is summoned to the High School DxD world by some ancient magic. He is seen as a powerful ally or a threat depending on who you ask. Rias takes it upon herself to figure out Naruto's intentions. As she gets to know him, she realizes that his values of friendship and protecting the weak are similar to her own. Together, they start a journey to stop a dark force that is rising in the DxD world, with Naruto teaching the devils some ninja techniques along the way.
His role could be that of a protector. Given his nature of protecting his friends in the Naruto series, he would likely do the same in the High School DxD world. He could protect Fem Kyuubi from those who might want to take advantage of her power. Also, he could be a bridge between the different species in the school, using his understanding of different types of people from his own world.
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.
In a Naruto, Ghost Rider, High School DxD fanfiction, a great storyline could be that the High School DxD world is in danger of being destroyed by an ancient evil. Naruto and Ghost Rider are brought in as the last hope. Naruto uses his friendship - building skills to gather allies among the students and factions, while Ghost Rider uses his power to fight off the minions of the ancient evil. As they progress, they discover that there are secrets in this world related to their own powers, and they must unlock them to save the day.
In a Naruto and High School DxD fanfiction, there could be a scenario where the protagonists of both stories meet in a neutral dimension. Issei from High School DxD might be intrigued by Naruto's ninja skills and determination. Naruto, in turn, could be curious about Issei's Sacred Gear. They could start training together, sharing their knowledge and skills, and ultimately have to face a common enemy that threatens both their worlds.
A possible plot could be that Naruto is somehow transported to the world of High School DxD. He's seen as a delinquent because he doesn't follow the school's rules which are very different from what he's used to in Konoha. He might start fights with some of the devils or fallen angels in the school who underestimate him. As the story progresses, he forms alliances with some of the students and they work together to solve problems in the school, like stopping a powerful enemy that threatens both the human and supernatural students.