It could be Voldemort who somehow follows Harry into the realm of the Morrigan. His dark magic could disrupt the balance there and make him a common enemy for both Harry and the Morrigan.
Perhaps an ancient enemy of the Morrigan, some dark entity from her own world, sees Harry as a way to get to the Morrigan. This entity could use Harry's presence to its advantage, trying to manipulate the situation to bring down the Morrigan. And Harry would have to figure out that he's being used and fight against this new threat.
It could still be Voldemort. Even though the focus is on Harry and Nagini, Voldemort is Nagini's master and the main source of evil in the Harry Potter world. He would likely try to stop Harry from getting too close to Nagini or from finding out any secrets Nagini might hold.
It could be a dark wizard who is jealous of the bond between Harry and Lily. This wizard might try to break their connection and use Lily's power for his own evil purposes. Maybe he wants to control Lily's magic, which is known to be strong, to achieve domination over the wizarding world.
There could be a group of anti - magic fanatics in the fanfiction. They see Byako as an abomination because of his strange powers that don't conform to the normal rules of wizarding magic. They also view the Hogwarts students' acceptance of Byako as a sign of the corruption of magic. So they set out to eliminate Byako and anyone who stands in their way.
Another possibility is that there is some sort of magical imbalance that only Harry and the Morrigan together can fix. Harry's knowledge of the wizarding world and the Morrigan's ancient and powerful magic combine to face a great evil that threatens both of their worlds. Harry has to learn to trust the Morrigan, even though she is a very different kind of magical being from what he has known.
It could be the person who sent the venomous snake after Harry Potter. Maybe a dark wizard who wants to harm Harry.
There might be a new character introduced in the fanfiction who is using the appearance of the Grim Reaper to cause chaos. This character could be a dark wizard who has found a way to mimic the Grim Reaper's powers and uses it to spread fear among the wizarding community. Harry would then have to figure out who this impostor is and stop their evil deeds.
Maybe it's a group of dark wizards who believe in a more extreme form of pure - blood ideology. They see Arcturus Black as a traitor for teaming up with Harry Potter, who is a half - blood. They plot to take over the wizarding world and eliminate anyone who doesn't fit their idea of a pure - blood wizard.
The main antagonist could be an old, corrupt house - elf. This house - elf was mistreated in the past at Hogwarts and has now turned to the dark side. It wants to bring chaos to Hogwarts and sees Lady Hogwarts as the key. It uses its knowledge of the school's hidden passages and secrets to plot against her. Harry Potter, being the defender of the underdog, tries to reason with the house - elf at first but when that fails, he has to use magic to stop it from harming Lady Hogwarts.
It could be Bellatrix Lestrange. Since she is a Death Eater and has a personal vendetta against Sirius, she would be a great antagonist. She might try to kill Sirius again and also target Harry to please Voldemort.
Maybe the main antagonist is an ancient magical being that has been awakened by the disturbance caused by Harry's exploration of the 'Mind of Magic'. This being believes that the wizarding world has strayed from the true path of magic and sees Harry as a symbol of this deviation. So, it decides to target Harry and try to bring back what it considers the 'pure' form of magic, even if it means destroying the current wizarding society.