There are two different types of jobs in this game, those that were available in the base game, FFXIV A Realm Reborn, and those introduced in the Heavensward expansion. Unfortunately, the one you're interested in is one of the HW expansion ones, which takes longer before you can unlock it.

ARR Jobs:
Get a base class to level 30 and its secondary to level 15 to unlock the job that extends the base class.
Gladiator (+Conjurer 15) -> Paladin
Marauder (+Gladiator 15) -> Warrior
Lancer (+Marauder 15) -> Dragoon
Pugilist (+Lancer 15) -> Monk
Rogue (+Pugilist 15) -> Ninja
Archer (+Pugilist 15) -> Bard
Thaumaturge (+Archer 15) -> Black Mage
Conjurer (+Arcanist 15) -> White Mage
Arcanist (+Thaumaturge 15) -> Summoner
Arcanist (+Conjurer 15) -> Scholar

HW Jobs:
Get to level 50 (as any ARR job, it doesn't really matter which), complete the entire ARR storyline. Buy the Heavensward expansion, and enter Ishgard, where you can unlock Machinist, Dark Knight or Astrologian. (These don't have a base class, and gain experience directly rather than using the level of their base class, so they're sort of like class and job rolled into one. They start off at level 30, though.)