Perhaps some corrupted Ministry of Magic officials could be the new antagonists. They could use the power of the Ministry to target Harry and his friends. Since they have the law on their side, Harry would have to find ways to fight them without directly breaking the law. He might need to use his influence among the students and the wizarding community to expose their corruption and undermine their authority.
It could be a group of dark wizards who have a different ideology from Voldemort. They might not be interested in pure - blood supremacy but rather in power for power's sake. They could be more cunning and use more psychological warfare against Harry, which would force him to fight in new ways.
Another option is that a new magical race or entity emerges as the antagonist. For example, a race from a different dimension that has its own set of rules and magic. They might see Harry and the wizarding world as a threat or as a source of power. Harry would then have to adapt his fighting style to deal with their unfamiliar magic and tactics.
In this fanfiction, perhaps Harry could use his wits more than magic. He might outsmart his enemies by setting up elaborate traps, like he did with the troll in the first year but on a much larger scale. He could use his knowledge of Hogwarts' secret passages to his advantage, leading his foes into dead - ends.
Another possibility is that an overzealous member of the Order who has gone too far in their methods of fighting Voldemort. Their extreme actions might make Harry think they have become as bad as the Death Eaters, so he starts to oppose them. For example, if this member starts using unethical spells on innocent people in the name of the greater good.
It's hard to say without more details about the fanfiction. But it could be some characters who benefit from Teddy not having rights, like power - hungry individuals or those with prejudiced views.
There could be a group of rogue witches and wizards who are against the current system in the wizarding world. They oppose the Ministry of Magic's rules and see Harry Potter as a symbol of the establishment they want to overthrow, so they become the antagonists.
It could be a group of rogue ninja who are after the Uzumaki's powerful sealing jutsu. They see it as a way to gain unlimited power and rule the ninja world, so they target the Uzumaki clan, which makes Naruto their main enemy as he stands in their way.
There could be a demonic entity in the new world. It might be awakened by Gilgamesh's arrival. This entity is used to having its way in the world and sees Gilgamesh as a new obstacle. It could possess other beings to attack Gilgamesh and use the chaos of the new world to its advantage.
Some pure - blood supremacist families who don't approve of their marriage could be antagonists. They might try to cause trouble for Harry and Luna, maybe by spreading false rumors or trying to undermine their work in the wizarding world.
The Ministry of Magic could be the antagonists. Since Harry is in a gang, they might see him as a threat to the order of the wizarding world. They could send Aurors after him and his gang mates, trying to arrest them and break up the gang.
It could be a group of power - hungry humans who see the Laguz as a resource to be exploited. They might want to use the Laguz's unique abilities for their own gain, like using their strength in labor or their magical abilities for warfare.
It could be a new group of rogue ninjas who have a vendetta against Konoha. They might be led by a powerful and cunning ninja who has a personal grudge against Naruto or the village in general.