FFXIV Endwalker: How to Unlock The Reaper

First and foremost, you need to own the Endwalker expansion if you want to play as a Reaper. The new jobs require you to level any Disciple of War or Magic job to level 70 before you can pick up the quest to unlock it. So if you're jumping into Final Fantasy 14 for the first time, you won't be able to play as a Reaper from the outset.  Instead you will need to play through the Main Story Quest or MSQ with another class until you hit 70.  Then... you can play The Reaper. 

With those requirements met, head to the Steps of Nald in Ul'dah and speak to the Flustered Attendant located at coordinates X:12.8 Y:8.6.