Drones require infrastructure to function. You've got to launch them from somewhere, and you have to land them somewhere, too. Infrastructure, as a general rule, is not secretive or stealthy, which can cause problems for the military, since they like being stealthy.
As far as the U.S. Navy goes, nothing is stealthier than a submarine, so turning one of those into a mobile drone launcher like the Naval Research Laboratory (NRL) just did makes perfect sense.
Submarines are already equipped with ways of sending missiles to the surface from depth. So all you really have to do to launch a drone from underwater is replace one of those missiles with a drone in a tube, fire it off, and then instead of engaging some sort of rocket motor, let the tube surface and then gently send the drone on its way.
Cormorant drone from Lockheed Martin, which is supposed to work as the following video: