Hunter by Mercedes Lackey

Synopsis (From Goodreads): They came after the Diseray. Some were terrors ripped from our collective imaginations, remnants of every mythology across the world. And some were like nothing anyone had ever dreamed up, even in their worst nightmares.

Monsters.

Long ago, the barriers between our world and the Otherworld were ripped open, and it’s taken centuries to bring back civilization in the wake of the catastrophe. Now, the luckiest Cits live in enclosed communities, behind walls that keep them safe from the hideous creatures fighting to break through. Others are not so lucky.

To Joyeaux Charmand, who has been a Hunter in her tight-knit mountain community since she was a child, every Cit without magic deserves her protection from dangerous Othersiders. Then she is called to Apex City, where the best Hunters are kept to protect the most important people…