The Exotic Quest can then be unlocked by talking to Lord Shaxx. He will then give you a couple of different quests to complete before you can upgrade your sword. Your first objective will involve killing 50 major or ultra enemies as well as 25 Guardians in the Crucible, and your second objective will require you to kill Ecthar, Sword of Oryx.
Once that’s completed, you’ll then have to pick which element you want your exotic sword to be infused with, and you’ll have to take the time to collect the material, which will take a while. If you want the Dark Drinker, you’ll have to infuse it with void.
You will have to collect the materials from battle as opposed to dismantling other weapons to obtain them, so this step will also require massive patience.
The last step in this process involves killing the warden of whatever material you’ve chosen your blade to be infused with. Only then will you be rewarded with the Dark Drinker.
If you made the decision to infuse your exotic sword with a different element, you’ll receive a sword different from the Dark Drinker — either the Raze Lighter or Bolt Caster.
Source : https://www.distractify.com/p/dark-drinker-destiny-2