Well, he could be a powerful antagonist. His skills and power from the Dragon Ball universe would make him a formidable foe in the High School DxD world. He might be interested in the power of the devils and angels there and try to take it for himself.
Goku Black could potentially enter the High School DxD world through a dimensional rift or some sort of magical accident. Once there, his Saiyan pride and his dark motives (from his own story) could lead to him either trying to take over the various factions in the DxD world or simply looking for a worthy opponent. He might interact with the main characters like Issei, perhaps seeing him as a target to prove his superiority or a potential ally in his own schemes.
Goku Black might become a sort of anti - hero. He has his own sense of justice (albeit a twisted one in his original story). In the High School DxD world, he could oppose some of the more corrupt elements of the different factions while also causing trouble for the main characters as they try to figure out his motives. For instance, he could see the way some devils treat humans in the DxD world and decide to take matters into his own hands, but not in a way that the main characters would necessarily approve of at first.
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.
His ki - based attacks would be a new and powerful addition. In High School DxD, most of the powers are related to magic, sacred gears, and demonic or angelic powers. Goku Black's ki blasts would be a completely different form of energy that could catch everyone off - guard.
There could be a really interesting fanfiction where the Queen of Blades from StarCraft gets inserted into the High School DxD universe. Maybe she could be a powerful new character in the school, causing all sorts of chaos or perhaps she teams up with the main characters to fight against a common enemy. It all depends on the creativity of the writer.
In a Naruto - High School DxD fanfiction, the power levels would be really interesting to explore. Naruto's sage mode and tailed - beast forms are extremely powerful. In the DxD world, there are different power systems like the Sacred Gears. It would be fascinating to see how Naruto's powers interact with the powers of the DxD characters. For example, could his Rasengan be enhanced by a Sacred Gear? Or how would he fare against a devil's magic?