There could be a new dark wizard or witch emerging in the wizarding world. This new villain might see Harry as a threat even in his running - away state. They could send their minions to capture Harry and Ginny, hoping to use Harry's fame and power for their own evil purposes.
The remaining Death Eaters could be the antagonists. Even though Voldemort is gone, there could be some who still hold a grudge against Harry and want to finish what their master started. They might track Harry and Ginny down as they run away, creating dangerous situations for the couple.
Voldemort and his Death Eaters would be obvious antagonists. They could be constantly hunting for Harry and Tonks as they are seen as threats to Voldemort's plans for total domination of the wizarding world.
Maybe some jealous students from Hogwarts or Beauxbatons. They don't like the idea of Harry and Fleur being together and running away to have an adventure. So they try to sabotage their plans, perhaps by spreading false rumors or even using minor hexes to slow them down on their journey.
One possible plot could be that they run away to escape some dark magic threat that Voldemort's remaining followers are planning. They might go into hiding in a remote wizarding village, where they have to learn to fend for themselves without the help of the Order of the Phoenix. Along the way, they could discover new magical abilities or ancient spells that help them in their fight against the dark forces.
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.
They might choose to run away secretly because they want to be alone together. They are in love, and the hustle and bustle of Hogwarts life doesn't give them enough privacy. So, they run away to a quiet place where they can enjoy each other's company without any interruptions.
Well, one possible plot could be that they run away to escape some sort of dark threat at Hogwarts. Maybe a new dark wizard has emerged and they feel that the school is no longer safe. So, they secretly gather some supplies, use magic to disguise their departure, and head off to a remote location like a hidden wizarding village in the mountains. There they try to find a way to fight the threat from afar while also exploring their relationship in a more private setting.
One reason could be to escape the public spotlight. After the war, Harry is a hero and Ginny is his girlfriend. They might feel overwhelmed by all the attention and want a quiet life, so they run away.
One reason could be to escape the constant media attention and pressure that comes with being in the wizarding world's spotlight. Harry especially has always had the eyes of the public on him, and running away might be a way to get some peace.
Voldemort or his remaining Death Eaters are often common antagonists. Even after his defeat in the original story, in dark fanfiction, they could come back in some form to target Harry and Ginny. For example, a Death Eater who escaped justice might seek revenge on Harry by harming Ginny.
It could be Voldemort or his remaining Death Eaters. Since they have always been the main antagonists in the Harry Potter universe, in this fanfiction they might still be the ones causing the danger that leads to Harry's sacrifice for Ginny.