It could be a corrupted prison guard. They might be taking advantage of the chaos in Azkaban to carry out their own evil plans, like stealing magic from the prisoners. Harry would have to stop them while also dealing with his own situation in the prison.
A group of Death Eater sympathizers within the Ministry could be the main antagonists. They still hold onto the old pure - blood supremacist ideals and see Hermione, a Muggle - born witch, as a threat. So they fabricate evidence against her and send her to Azkaban to send a message to all Muggle - borns that they are not welcome in the new wizarding order they are trying to create.
Maybe it's a new dark wizard or witch who has infiltrated the Ministry. They manage to manipulate the situation so that Hermione is blamed for their own misdeeds and sent to Azkaban. Their goal could be to cause chaos in the wizarding world and Hermione was the only one who could stop them.
Perhaps a new dark wizard or witch who has infiltrated the Ministry of Magic and made sure Harry was sent to Azkaban. This antagonist could be working towards a bigger plan to take over the wizarding world and sees Harry as a major threat even when he's locked up.
Another possibility is a new character that is unique to the other universe. This character could be jealous of Harry's arrival and the power he might bring from his own universe. So, this character tries to stop Harry from exploring and potentially changing the new universe.
One possible plot could be that Harry is wrongly accused of a serious crime within the wizarding world and is sent to Azkaban. There, he discovers a dark secret about the prison itself, like there being a hidden force controlling the Dementors. He has to use his skills and the loyalty of his friends to expose this secret and clear his name.
There might be a character who is secretly from the wizarding world but has turned to the dark side. This character could be after Harry in the Ouran setting, trying to use the chaos of the new environment to their advantage to get to Harry without being noticed by the Hogwarts professors.
It could be a new dark wizard that we haven't seen in the original series. This wizard might be jealous of Harry's fame and power and wants to eliminate him by making him disappear.
A jealous classmate could be the main antagonist. This person might be envious of Harry's popularity or the strange things that seem to always work out for him. They could start spreading rumors or trying to trip him up in his studies.
Obviously, Harry Potter himself is the central character. Hermione and Ron would most likely be involved too. They would probably try to find a way to get Harry out of Azkaban. Dumbledore might also play a role, perhaps guiding Hermione and Ron from behind the scenes or even trying to influence the wizarding court to re - evaluate Harry's case.
It could be a dark wizard who has infiltrated Hogwarts under a disguise. Percy might be the one to first suspect this wizard's true identity.