Cilia's right - additionally, foreigners specifically come to Eorzea just to become adventurers (read, the player's character), as the adventuring system is only an Eorzean institution and does not appear to exist anywhere else on Hydaelyn. This is all but confirmed when one of the Doman refugees stated that if Doma had had such a system in place it might have given them a sporting chance to drive back the Garlean invasion (which is the whole point adventuring was created as an occupation in Eorzea in the first place).

Either way, it's still likely Garlemald would have a secret network of sellswords and mercenaries (as they frequently make use of them in Eorzea), but the actual formalized Adventuring Guild seems to be very much only found in Eorzea.