Perhaps a corrupt Ministry official who wants to use dark magic for his own gain. He sees Harry and Hermione as threats to his plans and tries to stop their training by sending various obstacles their way. They then have to train even harder to overcome these challenges and expose the official's evil deeds.
In some cases, an ancient evil that has been awakened. This could be a powerful dark spirit or a long - forgotten dark magic creature. Harry and Hermione's training is focused on finding a way to defeat this ancient evil before it spreads its darkness across the wizarding world.
It could be a group of dark wizards who have escaped from Azkaban and formed a new dark alliance. They might be seeking revenge on Harry and Hermione for their role in defeating Voldemort.
Some pure - blood supremacists could also be antagonists. They may see Harry and Hermione, especially if Hermione is an heir as a Muggle - born, as a threat to their idea of a pure - blood - only wizarding society. They would do whatever it takes to stop them from rising to power and using the founders' legacy to promote equality and change in the wizarding world.
Voldemort or his Death Eaters could be antagonists. They might see the pregnancy as a way to manipulate or harm Harry and Hermione. For example, they could try to use the unborn child as a hostage or a weapon against them.
It could be the Death Eaters. They might not want Harry and Hermione to succeed in the ritual as it could be a threat to their dark plans. Or maybe some other dark wizards who are envious of the power that the ritual might bestow on Harry and Hermione.
Draco Malfoy is often an antagonist in such fanfictions. His family's beliefs in pure - blood supremacy could lead him to target Hermione, who is a Muggle - born witch. He might use his influence and his Slytherin friends to make her life difficult.
The Ministry of Magic itself could be an antagonist. If Fred and Hermione are running away because they've uncovered some sort of corruption or dark secret within the Ministry, the Ministry officials would want to stop them from spreading the truth.
One likely antagonist could be those who don't understand Cedric's possessiveness over Harry and see it as something abnormal or harmful. For example, some of Cedric's friends might think he's being too controlling and try to convince him to back off, which could create conflict. Another potential antagonist could be a character who has a crush on Harry and sees Cedric as an obstacle. They might try to break Cedric's hold on Harry, leading to a rivalry.
The obvious antagonists would be the Death Eaters. They are Voldemort's followers and are often causing trouble in the wizarding world. In this fanfiction, they might be the ones who have put Cedric in danger, either to lure Harry or for some other dark purpose.
Another possibility is a new dark wizard or witch who emerges and wants to prove themselves by taking on Harry and Ginny. This antagonist could be jealous of their fame and power and decides to target their DADA class to show that they are not as great as everyone thinks. They could try to undermine the students' confidence in Harry and Ginny's teaching.
One likely antagonist could be Draco Malfoy. He's from Daphne's social circle and might not approve of her being with Harry. He could try to expose their relationship out of jealousy or because of his pure - blood supremacist views.
Often, the goblins can be antagonists. If they have their own motives that conflict with Harry and Hermione's, like protecting a dark secret in the vaults or trying to take advantage of the situation for their own gain. Another possible antagonist could be a Death Eater who has infiltrated Gringotts to either steal something important or to ambush Harry and Hermione.