The Hunt

Kill 
Either Fura Bloodmouth or Garan Marethi will send the Dragonborn to a random location to kill an undercover Dawnguard spy pretending to be a travelling bard, merchant or pilgrim.

Example locations:
 * Falkreath at the Dead Man's Drink
 * Solitude at The Winking Skeever
 * Whiterun at The Bannered Mare
 * Ivarstead at the Vilemyr Inn
 * Kynesgrove at the Braidwood Inn

(Optional) Make it a discreet kill
Since these spies hang out at highly populated inns, a discreet kill, i.e. a kill that no other NPC is witness to, will be near impossible. But it is possible to persuade the spies to follow to a location of a "monster". Simply quick-travel with them to e.g. Castle Volkihar and kill them there.

Return to 
Returning to Fura or Garan may yield an item like:
 * Dwarven Shield of Shock Suppression
 * Ring of Major Archery
 * Steel Mace of Cowardice
 * Potion of Blood ×3

Die Jagd