"It is ... advisable that the teacher should understand, and even be able to criticize, the general principles upon which the whole educational system is formed and administered. He is not like a private soldier in an army, expected merely to obey, or like a cog in a wheel, expected merely to respond and transmit external energy; he must be an intelligent medium of action." -- John Dewey
However, autonomy is poorly understood by many teachers who advocate for it and also by the administrators who are suspicious of it. The reason for this is that autonomy is really different from being left alone.
Sure, the first step to developing autonomy is freedom from. Freedom from arbitrary constrictions. Freedom from micromanaging. Freedom from forces and interests that are obviously mis-educational. Administrators have a basic duty to protect teachers from these things so that they can explore and create.
Unfortunately, most conceptions of teaching autonomy stop there, but of course that sort of autonomy for teachers is not enough. Autonomy is more than freedom from constraint. Autonomy is positive freedom -- it is the freedom to act with purpose. Teacher autonomy (like individual autonomy) only finds its full expression within a purposeful community, and it is fuller yet when teachers are able out of their own practice (alongside students) create that purpose and feel responsible for the school community.
What then, is the role of the school administrator? As clear as I can figure it is to identify the ways in which the community is not yet autonomous or lacking purpose -- and also the teachers as individuals who have not yet found the full expression of their autonomous practice (or who have lost it somewhere along the way.) The administrator cannot ex nihilo create this purpose or autonomy, but must instead, through modeling, encouragement, listening, and communicating help teachers into autonomous community, actively and boldly clearing the path for it, and sometimes perhaps tracing the first steps.
If students are to learn to be free, active, bold, joyful, and creative, they must have in front of them on a regular basis adults who possess these qualities. Schooling is difficult work, and many adults lack the stamina or resilience to do this work and manifest these qualities. The best schools quickly identify the impediments to teachers being their full, best selves for their students, and eliminate them without pity.