Update 2: Here's our full Destiny 2 Outbreak Perfected guide!
Update: The quest has been cleared! And rather than Outbreak Prime, it rewards Outbreak Perfected, a redux version of the old pulse rifle. Clearing the mission also unlocks a Heroic version. Judging from the Whisper mission, the Heroic version will probably reward the Exotic Catalyst for Outbreak Perfected.
The latest Destiny 2 patch notes failed to mention the biggest addition in update 2.2.2: a new Exotic quest akin to the Whisper of the Worm. Nobody has cleared the quest at the time of this writing, so it's unclear what the reward is. That said, all signs point to Outbreak Prime, a pulse rifle from the original Destiny's Rise of Iron DLC which was also unlocked through an obscure quest.
As dataminer Eander said on Reddit, a gun that looks just like Outbreak Prime popped up in Destiny 2's backend today by way of a Catalyst entry. On top of that, the Fallen Transponder which starts the quest bears a striking resemblance to the SIVA tech tied to Outbreak Prime in the original Destiny.
You can start the new Exotic quest by playing the current Heroic Adventure on Titan, Bad Neighbors. A short ways into the mission, you'll come to a Hive Shrieker floating above a red-lit room. Go into the room and open the vault door on the left wall. Player reports suggest you must complete the Titan world quest Enemy of My Enemy in order to open this door. Here's a quick GIF to help you on your way:
We'll have a full guide on this quest posted soon. In the meantime, you can use this Reddit thread from Nyxara as a guide. Nearest I can tell, you need to collect six nodes from different Lost Sectors in order to unlock a timed, 690-Power, three-player mission called Zero Hour. You start the mission in a basement on the Farm, but it's actually set in the old Tower.
From what I've seen of this mission on various Twitch streams, it's filled with tough enemies, puzzles, and platforming challenges, not unlike the Whisper of the Worm mission. You'll want to be at least 680 Power, and your party of three should bring solar, arc, and void weapons to break enemy shields. Godspeed.
Between this and the first - and probably final - Riven solo kill, today's been a wild day for Destiny 2.