Enki could keep one shirei on his arrival to Khu Ioduan. He will also be able to earn back more with rewards later on in the game. While the question about subduing native creatures is conditional on whether or not he can keep them, we thought it best to still address it.

While the present bestiary doesn't include any creatures sentient enough to enter into a contract with Enki, this will likely change in the future as more places and their inhabitants are revealed! Gaining a contract with these creatures would operate the same way as earning back his original shirei - with rewards. Hope that helps!