When it comes to performance art, there's no position more powerful than the director. Your actors may be responsible for making the audience laugh/cry/feel confused and frustrated, but it's the director who makes sure they do it on the right spot, at the right time, with the right motivation. The same goes with the lighting, sound, costume design, and everything else―it only works when it is planned and coordinated.
A.k.a. Directed (oh, so that's where that comes from).
Your power isn't just a personal power over the theatrical underlings; the play itself, up to a certain level based on script and financing, will be created with your own artistic vision in mind. Yes, the theatre is a collaborative process, but every ship needs a captain and the captain says where the ship will sail.
That means, if you want to set your production of Macbeth in a post-apocalyptic wasteland (sounds cool to us), the costume designer better come up with a sweet raider outfit for Lady Mac.