A Jarl's Justice is a side quest in Skyrim: Dawnguard.
It is only available to Dawnguards.
The quest A Jarl's Justice starts in Fort Dawnguard
A Jarl's Justice is given by Isran, the leader of the Dawnguard.
Isran has sent me to Dawnstar to warn Skald of a vampire masquerading as a visiting advisor to his court. I am to destroy the beast. If I fail to secure Skald's permission first, the guards will consider it a murder.
Warn Skald about the vampire threat. (NOTE: Could be another Jarl, chosen at Random)
Find evidence linked to the vampire
Talk to the Jarl in Dawnstar (Or other random city), but evidence is required before anything can be done. You can find this evidence by pickpocketing the Visiting Advisor and finding Orders. The Visitor Advisor is sitting outside the Jarl's court.
Pickpocket the Visiting Advisor (you should be able to pickpocket him even when detected)
Then bring orders to the Jarl. The Jarl will give you permission to kill the impostor and tell you that the guards won't interfere.
Kill the Visiting Advisor.
Go back to Fort Dawnguard and talk to Isran.