Perhaps it's a corrupted Hogwarts professor. In this fanfiction, a teacher could have been influenced by the dark side and decides to oppose Harry's new path. They could be using their position at Hogwarts to spread dark magic teachings or to manipulate students against Harry. They would be a more insidious antagonist as they are operating from within the very institution that is supposed to be a safe haven for Harry.
It could still be Voldemort, but in a different form. Maybe he has a new power or a different plan this time. Since it's a new chance, he might have found a way to come back even stronger and more devious than before.
It could still be Voldemort. Even though Harry has a second chance, Voldemort is still a major threat in the wizarding world. His presence and his Death Eaters would continue to be the main source of danger, and Harry would need to use his second chance wisely to defeat him once and for all.
It could be Harry Potter himself. Given all the hardships he faced in the original series, a second chance would open up a whole new world of possibilities for him. He could use this chance to prevent some of the tragedies that occurred, like the deaths of his friends or mentors.
It could be a distant relative of Voldemort who has been biding their time in the shadows. They might have a vendetta against the Potter family for what happened to Voldemort. This relative could be secretly gathering followers and planning to strike at the second child when they least expect it.
It could be a rogue Death Eater who decides to carry on Voldemort's legacy in a more extreme way. This Death Eater might have some new and terrifying dark magic up their sleeve.
It could be a dark wizard who has a vendetta against the Weasley family. Since the twins are part of the Weasleys, this dark wizard targets them. Maybe he blames the Weasleys for something that happened in the past, and the twins, being the more adventurous and visible members of the family, become the main targets.
Maybe a group of pure - blood supremacists who didn't like the changes that Harry brought to the wizarding world after the war. They believe that the old ways of pure - blood dominance should be restored and will stop at nothing to oppose Harry's new beginning, which includes more equality among all wizards and witches.
It could be a new dark wizard or witch who rises to power. Maybe someone who was once in Voldemort's shadow but now sees an opportunity with Voldemort gone (in this new fanfiction scenario where Snape has a second chance). This character could oppose Snape's attempts to reform the wizarding world and bring about a new era of peace and magic.
Perhaps a long - lost relative of the Potter family who feels they were unjustly excluded from inheriting the manor. This relative could be jealous of Harry's status and the wealth associated with the manor. They might use dark magic to try and claim what they think is rightfully theirs, leading to a battle of magic and loyalty within the Potter family and among Harry's friends.
Maybe there could be a new antagonist, a dark shapeshifter who is jealous of Harry's power. This antagonist could be an old wizard who has been in hiding for centuries, waiting for the right time to emerge and take over the wizarding world. He sees Harry as a threat to his plans and tries to eliminate him.