Spirits out for revenge are normally referred to as avengers or revengers by paranormal investigators. Seeking justice is what theses type of ghosts are about. They are trying to right a wrong or avenge a death.
This type of spirit may appear at the scene of a crime or make itself known to someone it trusted while it was alive. They can cause cold spots, sudden drops in temperature, and sometimes act like poltergeists.
Mediums are able to communicate with the vengeful spirit and convince them to reach a fair conclusion for everyone involved. The most famous example of an Avenger is the fictional 1990 film Ghost played by Patrick Swayze.