Perhaps an ancient evil that Gryffindor once sealed away is starting to break free. This entity sees the descendant as a threat because they have the potential to reseal it. So, it tries to corrupt the descendant or stop them in any way possible.
Perhaps an old enemy who has infiltrated Gryffindor in disguise. They use their influence to make the Gryffindors believe that Harry is a danger. They could be a Death Eater or a follower of Voldemort who has found a way to get into Gryffindor and manipulate the students' minds, causing them to betray Harry.
Perhaps a group of pure - blood supremacists could be the main antagonists. They see the Peverell descendant as a threat to their ideas of a pure - blood - only wizarding world. They might try to undermine the descendant at every turn, spreading false rumors and trying to isolate them from the rest of the wizarding community.
A dark force that has the ability to influence the minds of Gryffindor members. This could be a powerful and ancient magic or a new form of dark magic. It turns the house against Harry without them fully realizing it, making the collective Gryffindor house, under this influence, seem like the antagonist.
It could be a dark wizard who also has some form of time - related power. Maybe he wants to use time to his advantage to take over the wizarding world. For instance, he could go back in time to eliminate the founders of Hogwarts so that he can rewrite the rules of magic for his own evil purposes.
One interesting plot could be that the descendant discovers a hidden chamber in Hogwarts that was sealed by Gryffindor himself. Inside, there are ancient spells and secrets that could change the wizarding world. The descendant has to battle dark forces who also want to get their hands on these secrets.
Well, Harry Potter himself could be a possible heir. He already has so many Gryffindor - like qualities. His courage and loyalty make him a strong candidate.
Ron Weasley can also be thought of as an alpha in certain fanfictions. He has his own brand of loyalty and courage. When his friends are in trouble, he steps up. His growth throughout the series, from a sometimes - insecure boy to a confident young man, gives him alpha - like qualities in the context of Gryffindor.
Another potential antagonist could be a jealous rival within Slytherin. This character might be envious of the 'Prince of Slytherin's status and popularity and would stop at nothing to bring him down. This could lead to a lot of internal Slytherin house drama and power struggles in the fanfic.
Maybe it's a new Gryffindor student who has been influenced by the wrong people. This new student doesn't really know Harry well and is easily convinced by some anti - Harry propaganda within the school. So they become the main antagonist in the story and lead the attack on Harry.
It could be a power - hungry Slytherin who doesn't like that Regulus is showing an interest in Gryffindor values. This Slytherin might see it as a betrayal to their house and try to stop Regulus by any means necessary, even if it means using dark magic.