Lex Luthor from Supergirl's world could be the villain. He could somehow find a way to travel to the wizarding world and team up with some dark wizards. He wants to use magic to enhance his power and take over both worlds. Supergirl and Harry Potter would have to stop his evil plans.
A new villain could be created, like a powerful sorcerer who has some Kryptonian DNA. He wants to use his combined powers of magic and super - abilities to rule the universe. He would be a formidable foe for both Supergirl and Harry Potter as he can use magic to counter Supergirl's powers and super - strength to overpower Harry and his friends.
Reverse - Flash could be really interesting. He could manipulate time in ways that not only affect Flash but also Supergirl. For example, he could go back in time and prevent Supergirl from arriving on Earth, which would change the whole timeline. Flash would then have to convince her to come to Earth again while also dealing with Reverse - Flash.
The Reverse Flash could be an exciting villain in a Supergirl Arrow crossover. His ability to move at super - speeds would make him a formidable opponent for Supergirl. He could also mess with Arrow's timeline, creating chaos in both their worlds. Imagine him going back in time to prevent Supergirl from arriving on Earth or changing events that led to Arrow becoming a vigilante. His manipulative nature and his connection to the Speed Force would bring a whole new level of complexity to the crossover story.
Lex Luthor could be a great villain. He might be jealous of Supergirl's powers and see Flash as an obstacle in his plan to defeat her. He could use his scientific knowledge to create some sort of weapon that targets both speedsters and Kryptonians.
Darth Vader could be a great main villain. His dark power and iconic status in Star Wars would make him a formidable foe for Supergirl. He could see her as a threat to the Empire's rule and try to eliminate her. His mastery of the Force and lightsaber skills would put Supergirl in a tough fight, especially if she's not familiar with the ways of the Force at first.
It could be a Death Eater who has somehow made a pact with a powerful force from Scorpian's world. This villain would be extremely dangerous as they'd combine the dark magic of the Harry Potter universe with the unknown and potentially deadly powers from Scorpian's realm.
A Supergirl and Harry Potter crossover fanfiction could be really exciting. It might involve Supergirl somehow ending up in the wizarding world. Maybe she uses her superpowers to help in a Quidditch match, flying faster than any broom. Or she could use her heat vision to defend Hogwarts from a dark wizard's attack.
Perhaps an interdimensional villain. This villain could be causing disruptions in both The Flash's and Supergirl's dimensions, forcing them to meet and join forces to stop it. The villain could have powers that are a challenge for both of their unique abilities.
The characters in Harry Potter might be a bit shocked at first. Hermione would probably be very curious about Supergirl's powers and how they work. Ron might be a bit jealous at first but would eventually come around. Dumbledore, if he were still alive, would likely see it as an opportunity for the wizarding world to expand its horizons. In the Supergirl world, Kara's friends like Alex would be protective at first but would see Harry's good heart. J'onn J'onzz would be intrigued by the magic and how it could be used in their fight against evil.
A fallen angel who is jealous of Lucifer's newfound friendship with Supergirl and his life on Earth. This fallen angel decides to cause destruction on Earth to get back at Lucifer and also sees Supergirl as a threat to his plans of ruling over the mortals.
Another option could be a new character created specifically for this crossover. This character could be a wizard who has studied the ninja arts and has become corrupted by power. He could start by causing chaos in the wizarding world, using his magic to mimic some of the more dangerous ninja techniques. Then, he could set his sights on the ninja world, seeing it as another source of power to be conquered. Fem Naruto and Harry Potter would have to put aside their differences and work together to stop him.