Perhaps a dark wizard from the Harry Potter universe who has heard about the Cullens' unique vampire abilities and wants to harness that power for himself. He could be a follower of Voldemort who escaped the final battle and is now looking for new ways to gain power. So he targets the Cullens, thinking their powers can help him rule both the wizarding and vampire worlds, and Harry has to stop him.
There could be a group of werewolves who have a long - standing feud with the Cullens. They see the Cullens as a threat to their territory or way of life. They team up with a rogue wizard who provides them with magical items and spells to attack the Cullens. Harry Potter then steps in to save the Cullens from this combined threat of werewolves and the rogue wizard.
The Volturi could be the main antagonists. They are the powerful vampire leaders in the Twilight world and might not like the idea of a wizard like Harry being around the Cullens. They could see Harry's magic as a threat to their vampire - only world.
Maybe a new character could be created as the main antagonist. A dark wizard who has infiltrated the Capitol and is using the Hunger Games as a means to create chaos and destruction. He could be more powerful than Voldemort in some ways and would be a great challenge for Harry and Katniss to overcome.
It could be a powerful dark wizard who has somehow made his way into the Avengers' universe. Maybe a wizard who was banished from the wizarding world in Harry's universe and has now joined forces with some of the Avengers' villains.
It could be a dark wizard who has his eyes on Cintra's powerful magical artifacts. He wants to use them to gain more power and is willing to destroy Cintra to get them.
It could be a rogue Death Eater who has escaped from Azkaban. This Death Eater might be desperate to regain his power and believes that unicorn blood will give him the strength he needs. So he sets out to capture a unicorn in the Forbidden Forest, which is where Harry comes in to stop him.
It could be a dark wizard who has a vendetta against goblins. This wizard might see goblins as a source of power or wealth and wants to enslave them. So when Harry tries to save the goblin, this dark wizard becomes the main obstacle.
One possible plot could be that a powerful dark wizard has set his sights on the Cullens for some reason, maybe to use their vampire powers for his own evil deeds. Harry, being the hero he is, senses this danger through his connection to the magical world. He then teams up with the Cullens, teaching them some basic wizarding defenses like Shield Charms. He also uses his own powerful magic, such as the Killing Curse in a defensive way if necessary, to save the Cullens from the clutches of this dark wizard.
It could be some dark wizards who want to use the centaur's parts for potions. They might be following some ancient, dark magic recipe that requires centaur hair or hooves. So they hunt down the centaur, but Harry gets in their way.
It could be an ancient dark magic artifact. The artifact has a hold on Bellatrix, and in a way, it's the 'enemy' that Harry has to defeat to save her. The artifact might be trying to use Bellatrix to carry out some dark plan, like opening a portal to a world full of dark creatures. Harry has to figure out how to break the connection between Bellatrix and the artifact while also fending off the artifact's attacks.
A group of dark creatures like Dementors could be the antagonists. They might be after the young goblin because goblins have a unique life force that can sustain Dementors in a way other prey cannot. Harry Potter would have to face his own fears while using powerful Patronus magic to drive the Dementors away and save the goblin.