You need to craft one of the outlaw weapons, either a Sandstorm, Sidewinder, or Vanquisher
After interrogating Vehn Terev in Hunting the Archon, head to the Kadara Slums. On the upper floors, next to the second-story entrance to Tartarus, there will be a Disillusioned Outlaw who calls you over.
Use any Research Station, on the docks at Kadara Port or on the Tempest, to craft one of three Outlaw weapons, the Sandstorm (Milky Way assault rifle), Sidewinder (Milky Way pistol), or Vanquisher (Milky Way sniper rifle). First research the weapon, then use the development menu for creating it.
Bug: The task auto-completes when the conversation is over. You receive no xp reward, and task is listed among Completed Missions. Verified after the release of patch 1.10.