You mentioned a century old victim, which means the targeted young woman can not be family to the female vampire.
Since she would have outlived all possible family in 100 years.
So WHY she aims to protect the young woman (the serial killer's next target?) is unclear
She's chased down by three segments:
police, vampire hunters and a victim
Which seems useless
Why she doesn't take care of the vampire hunters (in her own way) remains a mystery to me.
I don't know why they are even mentioned here..
Unless they have their respective places in the plot, I'd suggest you mix and match to create more interesting characters, like-
1. A Vampire cop (her victim disguised as a cop leading the search against her) or
2. Vampire hunter cop (human cop known for his traditional ways to deal with the mysterious cases)
One thing's for sure
The serial killer is your antagonist
But are you sure he can handle a vampire headed his way?
For all I know he's still a wimpy human to me and the day he meets the vampire, your story will come to an end.
If he's smart enough to evade her at each step....well, why would anyone watch something so un-cinematic?