One possible plot could be that Naruto discovers he has exorcist powers in addition to his ninja abilities. He then has to learn how to control and use these new powers while still dealing with the threats in his ninja world.
I'm not sure specifically which 'Naruto is a exorcist' fanfiction is great. You could try searching on popular fanfiction websites like Fanfiction.net or Archive of Our Own. There might be some interesting crossovers there.
Yes, there might be. The Naruto and Blue Exorcist fandoms are both quite large, and it's not uncommon for fans to create crossover fanfictions. You can try searching on popular fanfiction websites like Fanfiction.net or Archive of Our Own.
Power-ups are a common theme. Since Naruto already has his ninja powers and then enters the DxD world with its own set of powers like Sacred Gears, a lot of fanfics focus on how he combines or enhances these powers. For example, he might learn to use his chakra in new ways because of the DxD environment.
A possible fanfiction could involve a character from Naruto, say Sasuke, ending up in the Twin Star Exorcist world. Sasuke, with his Sharingan and powerful jutsu, could be mistaken for an exorcist at first. He then has to figure out how to get back to his own world while also dealing with the Kegare. Or perhaps Naruto and Rokuro could meet in a strange in - between world. They could team up to fight a common enemy that is a threat to both their worlds.
Naruto's chakra-based powers could potentially enhance the exorcist powers. For example, his Rasengan, which is a concentrated form of chakra, might be able to disrupt a demon's energy in a way that normal exorcist attacks can't. His shadow clone jutsu could also be used for reconnaissance in the world of Blue Exorcist, helping the exorcists plan their attacks better.
The Occult Research Club members in general would be his allies. They are used to dealing with all sorts of supernatural situations, and Naruto's skills would be a great addition to their group. Kiba Yuuto, for instance, could bond with Naruto over their combat - loving natures. They could train together and come up with new strategies for fighting enemies in the DxD world, whether they are devils, fallen angels or other threats.
One likely main antagonist could be a powerful demon lord who is trying to break through the barriers between the spirit world and the human world. This demon lord would be a major threat to Naruto and his harem, and they would have to use all their combined skills to stop it.
Another plotline might be Naruto having to choose between different girls in the harem while also dealing with the challenges of exorcising powerful entities. He might face a situation where saving one girl means sacrificing his progress in exorcising a major demon, creating a moral dilemma.
One possible plot could be Naruto being summoned to the DxD world by some sort of magical accident. He could then use his ninja skills, like his shadow clone jutsu, in unique ways to combat the devils and exorcise evil spirits. For example, his clones could be used to surround and confuse enemies during an exorcism battle.