Well, we already know Arcanist and Musketeer are classes awaiting to be unlocked in the near future, after all the issues are dealt with, of course. However, here are some ideas I've conjured up through my experiences with the game and it's lore.
Chocobo Handler/Jockey (Disciple of Beasts)
This would/could be a completely new class all together and a unique addition for Chocobos to have a larger role than any other FF game. Dealing with
breeding, raising, racing, and riding of Chocobos as a class in itself. But, just like any other class, you can swap abilities to customize your character, so you can ride a Chocobo as any class. However, to advance your bird skills, and race them etc, you need to switch back to that class for all the interactions.
- Earning money, rare items for crafters to use (I.E. Golden Chocobo eggs, feathers, etc.) and obtaining other rare items only found by digging and racing in races with the bird, not found in any other class.
- Class quests would enable you to dive deeper in the Chocobo lore in Eorzea and also earn a license to race them and such and better equip your bird, by completing the quests and then purchasing the license and new abilites with enough guild points.
- Breeding them would enable you to earn different colored birds with more abilities. You can also buy new gear for them to race better and become stronger/faster out in the field. Crafters could play a large interaction role by making you the necessary gear for them (I.E. Saddles, armored helmets for the bird, protected leg guards, and stat enhancing meals cooked for them by culinarians (Gyhshal Greens and other healthy varieties to improve your birds overall stats).
- I'm guessing at a higher rank in this class you can summon your personal, customized Chocobo with a Choco Whistle and store items on it via Choco Retainer (200 bag space). You can buy a bigger bag with Guild Points and from crafters crafting them for you, and then ride your mount anywhere around the world. Choco Whistles need repairs when you use them too much.
I have some more interesting ideas, but this is just a start for the developers to get some ideas and brainstorm a bit.