Greenlees was appointed executive director of the Crafts Council in 2006. The national charity for crafts promotes the value of craft and making to society. It is mainly based in London and has its own gallery. The Council supports craft workers through registering them in its directory, presents exhibitions, convenes Crafts UK (a network of interested organisations) and undertakes research and advocacy. This element of the Council’s mission is important to Greenlees, who has described how the field “creates opportunities” for disabled people to be “economically active” and “creatively fulfilled”. She has had a lifelong involvement in the sector, having begun her career as a visual arts curator. Greenlees subsequently built up experience in senior, international and political roles such as at the London Centre for Arts and Cultural Enterprise, the South London Gallery and the World Crafts Council Europe. Between 2000 and 2004, she was the cultural strategy manager for Ken Livingstone, then Mayor of London.
