The NEXTOWER H2020 EU project investigates the possibility of using liquid lead as heat storage medium for high-temperature Thermal Energy Storage (TES) in concentrated solar power plants. To that end, within such project, a demonstration TES unit named SOLEAD (SOlar LEAd Demonstrator) is being developed and will be coupled with an open volumetric air receiver in a solar tower CSP system. The SOLEAD demonstrator will be built and operated at the Plataforma Solar de Almeria (Spain) as a result of the project effort. In the present paper, the conceptual design of the SOLEAD demonstrator is illustrated in details. Basically, SOLEAD is a single-tank thermocline TES system using a pool of liquid lead as heat storage medium. The receiver collects energy from the solar field and heats atmospheric air up to 900°C; the hot air is then used to thermally charge the SOLEAD system through an air-lead primary heat exchanger located in the lower part of the lead pool. In particular, one of the goals of the design is to reach a temperature stratification from 600°C (lower part) to 750°C (upper part), which cannot be achieved with the common molten salt mixtures used in commercial TES systems for CSP applications. The thermal stratification is obtained by positioning the primary heat exchanger in the bottom part of the pool and by exploiting the buoyancy forces to promote natural circulation in the pool. This method avoids the use of a pump with an impeller and a proper orifice calibration allows to attain in the average the required mass flow rate and temperature drop in the system. The design of the air-lead primary heat exchanger is innovative and challenging due to the poor heat transfer properties of the atmospheric air at 900°C. The Heat exchanger is counter-current bayonet type with the air on the bayonet side and the lead on the shell side. The design of the heat exchanger was performed by a large use of CFD tools and modelling and includes a riser to guide the flow path and to bring the hot fluid in the top part of the pool.