There are 2 additional slots in the stable.

Integrating hunter / warlock pet management into the new mount and companion UI has certainly come up already. Let's give the new UI a whirl and see if it works and then we can consider if it makes sense to integrate the stable or anything else into it.

Finally!  Really hope the plan to "integrate" the stable with the new mount/pet tab works out!  Like that dun nid to hearth back just to change pet!