You'll have to reach level 50 and complete the main storyline of A Realm Reborn before you can even access most of the features of the Heavensward expansion (the regions and quests it added, or the additional jobs).

The only significant exception is the Au Ra race (the characters with horns and patches of scales here and there). If you want to create an Au Ra character you'll need both the game and expansion. That's the only thing the expansion gives you right from the beginning.