A human who has been secretly observing the vampires and werewolves all along and has developed psychic powers as a result of their proximity to the supernatural. This character could be the one to bridge the gap between the different species and bring about a new era in the twilight world.
It could be a new character, like a young girl who has just moved to Forks and discovers she has psychic powers. She then gets caught up in the existing drama of the twilight world.
Perhaps an old character from the twilight series could be given psychic powers. For instance, Alice could develop a new level of psychic ability that allows her to not only see the future but also manipulate it on a small scale. This would add a whole new dimension to her character and the story.
It could be someone completely new. A character that the author creates to disrupt the status quo in the Twilight universe. This new character might have unique powers or abilities that change the course of the story.
Perhaps it could be a minor character from Twilight who somehow ends up in a situation where they are kidnapped by a creeper. This would give the writer a chance to explore that character more deeply and in a completely different context. For example, a character like Jessica from Twilight could be the main character. She's not a central figure in the original story, but in this fanfiction, she could have a whole new adventure.
It could be a new character entirely. Maybe a young vampire who was turned recently and is still adjusting to the 'alive inside' state of being undead. This character could struggle with the morality of being a vampire while also trying to fit into the Twilight world's complex social structure.
An old werewolf who has decided to retire from the pack life and goes on a trip to all the places that were important to the werewolves in the Twilight story. Along the way, they might run into some vampires and have to face old prejudices and form new alliances.
Edward Cullen could be a great main character. Since he is already a part of the Cullen family who loves baseball, he could be the one to hit a crucial home run. Maybe this home run is what saves Bella from some sort of danger during a baseball - related event. For example, the Volturi might be there to cause trouble during a game, and Edward's home run distracts them long enough for Bella to get to safety.
Another option could be Jacob. As a werewolf, he has a connection to the spiritual side of the Twilight world. He might be the one to discover the hauntings first and have to figure out how to deal with them, especially if they pose a threat to his pack or the people he cares about in Forks.
A new character could be introduced as the main character. This character could move to Forks and be unaware of the supernatural world there. Their arrival could trigger a series of events that force the existing Twilight characters to have a fresh start in how they deal with their secrets and relationships.
A new villain could be introduced. For example, a powerful trainer who is jealous of Ash's new powers. This trainer wants to defeat Ash and steal his aura psychic abilities to become the most powerful trainer in the world.
A young vampire who was recently turned against their will. They are lonely because they miss their human life and family, and they don't fit in with the other vampires yet. They are constantly haunted by nightmares of their transformation and the life they've lost.
A human friend of Bella's could be the main character. Someone who is not fully aware of the vampire - werewolf world at first. When they find the crown at Christmas, they are drawn into this hidden world. They might be the key to uniting the different factions because of their outsider perspective and the power of the crown they possess.