This report describes the conceptual design of a proposed free electron laser test facility called CLARA that will be a major upgrade to the existing VELA accelerator test facility at Daresbury Laboratory in the UK. CLARA will be able to test a number of new free electron laser schemes that have been proposed but require a proof of principle experiment to confirm that they perform as predicted. The primary focus of CLARA will be on ultra short photon pulse generation which will take free electron lasers into a whole new regime, enabling a new area of photon science to emerge.