A person who seeks revenge can be called an avenger. If you pay your brother back for eating all the cookies by finishing the last of his ice cream, you are an avenger of sorts.
You may have heard of the comic book, TV, and movie superheroes called "The Avengers," but they're only one group of famous literary avengers. You could also call Shakespeare's Hamlet, who gets revenge for his father's death, an avenger. Most of the characters in the Greek classic "The Iliad" are avengers, too. The Old French root, avengier, means "to take revenge."