Sanhedrin 82 - Extrajudicial Executions
There are special cases of transgressions that do not involve a court action, but are carried out either by the zealots or by Kohanim in the Temple.
One who steals service vessels in the Temple; one who blasphemes by a supernatural force, saying "Let the supernatural force (that is, the idol) smite him (the blasphemer's enemy), his Creator, and his Provider; and one who cohabits with an Aramean woman - zealots may kill him.
If a zealot comes to ask about this ruling, he is not told about it, and not given the permission. He has to know it from before and then take the risk in his own hands. Furthermore, he can only do it while the sinner is engaged in his sin. If the sinner stops, and the zealot kills him then, the zealot is responsible for murder.
If a Kohen serves in the Temple in the state of ritual impurity, young Kohanim remove him outside the Courtyard and split open his skull with clubs.
Art: Paul Cezanne - Vessels Fruit And Cloth In Front Of A Chest