The Adeptus Arbites are the central law enforcement agency of the Imperium of Man. Whereas local officials will handle most ordinary crimes such as thievery and murder, the Arbites are concerned primarily with crimes against the Imperium itself, whether it be violations of edicts, attempts at revolution, or the occasional heretical cult.
In TTS, the Arbites are shown to be extremely stubborn and obsessed with the law, taking it to the extreme by enforcing rules regardless of common sense or practicality. They will even spend multiple generations trying to judge a case before punishing the distant descendants of the original perpetrator. The Grand Provost Marshal in particular is guilty of creating laws that are extremely detrimental to the well-being of other people.