Many supplementary and complementary schools operating in the United Kingdom and other countries have connections and relationships with religious organisations. However, there is considerable variety and complexity in these links and connections. Amidst some public concerns about these schools and as so little is known about them compared with other school sectors, a new heuristic device is offered to support leadership practice in supplementary and mainstream schools, and to encourage research particularly in the areas of governance, leadership and management. The need for this heuristic is made all the more urgent because of the disengagement of the state, at various levels, from appreciation of and support for the work of these schools, compounded by the lack of knowledge and understanding of their governance, leadership and management in particular. The exclusion of supplementary schools with religious links from future research and school partnerships needs to be avoided.