If you craft, supply/provision missions are a good source for both GC Seals and crafting XP, though they're limited to once per day per class. (The amount of seals you get varies with the level of item, so this may not seem like much at first but becomes an increasingly good source the higher your DoH classes level up.) And once you reach Sergeant Second Class, you'll unlock expert delivery missions, which let you turn in certain types of excess gear (typically dungeon drops).

The GC portion of your hunting log gives some good GC Seal bonuses. (Plus the first couple tiers of it you're going to need to finish for a couple later promotions anyway, as Sagittarian mentioned.)

And FATEs are still a good unlimited source.