For beast tribe quests, you'll need to visit the three Grand Company buildings and pick up some Lv40-ish quests (plus one Lv.1 quest for the crafting-based Ixals) that will unlock daily quests from "friendly" outcast groups of the beast tribes: sylphs, Ixal, Amalj'aa, Sahagin and kobolds.

(You might have already stumbled across some of them while questing, and the sylphs are the same group from earlier in the MSQ.)

As well as EXP, you unlock access to mounts, minions, crafting materials and dyes you can't buy elsewhere.