I read this book about UK drone pilots last year..
I can't remember the full details of it all, but it depends on the situation. If they are called in to support troops in contact I think it's treated pretty much like a normal manned fighter/bomber aircraft. The pilot or person in charge of the weapons makes the final call on if they release a weapon.
In other suituations where there isn't an immediate risk then it gets escalated to the aporiate level of government. One of the examples I remember was a tank that was being used by daesh. It has been seen in combat but the drone on station had used all its weapons. It kept an eye on it, followed it back to where they were storing it. Next drone came on station and was armed, but they had to wait for permission destroy it.