To unlock Reaper you must complete the quest The Killer Instinct which can be started by speaking to the Flustered Attendant in Ul’dah – Steps of Nald (X:12.8 Y:8.6).
Flustered Attendant Location
This quest has a requirement of level 70, so you will need to have at least one DPS job at Level 70 or higher in order to accept it. A blue quest marker (with a plus sign next to it) will appear above the Flustered Attendant.
The Killer Instinct quest introduces you to the main characters of the Reaper job questline and rewards you with a starting set of Reaper gear. You’ll get a full set of Level 70 (item level 385) armor, a starting Level 70 weapon and a job crystal.
You will then unlock a significant number of abilities. Make sure to read all the tooltips for each skill ts get a feel for the classes rotation.
You may continuie the Quest Line by picking up the Quest The Harvest Begins from Drusillia.