When leaders are admonished to 'be authentic' they sometimes translate that as 'stick to your knitting' or 'to thine own self be true.' Actually, leaders must always aspire to being better at what they do, and that means changing.
HBR.org: The Authenticity Paradox, 2015-Jan by Herminia Ibarra
When we look only within for answers, we inadvertently reinforce old ways of seeing the world and outdated views of ourselves. Without the benefit of what I call outsight—the valuable external perspective we get from experimenting with new leadership behaviors—habitual patterns of thought and action fence us in. To begin thinking like leaders, we must first act: plunge ourselves into new projects and activities, interact with very different kinds of people, and experiment with new ways of getting things done. Especially in times of transition and uncertainty, thinking and introspection should follow experience—not vice versa. Action changes who we are and what we believe is worth doing.