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A ringed accretion disc (RAD) models a cluster of axis-symmetric co-rotating and/or counter-rotating tori orbiting in the equatorial plane of a central Kerr supermassive black hole. We discuss the time evolution of such a ringed disc within the general relativity framework. Our analysis presents a study of the evolving RAD properties using a thin-disc scheme and solving a diffusion-like evolution equation for a RAD in the Kerr space-time. In the first stage of evolution, there is the inter-disc interaction where the individual rings spread inwardly and outwardly, levelling the structure and forming a single distribution with maximum density determined by the initial spread of the component rings. Time-scales are dependent on viscosity prescriptions. The early time luminosity, dominated by the dynamics of the inner ringed structure, shows a clear mark of the inner ringed structure. The RAD eventually reaches a single disc phase, building accretion to the inner edge regulated by the inner edge boundary conditions. The late-time luminosity associated with the ringed disc follows a power law decline for the final single disc. In the sideline of this analysis, we also considered a modified prescription mimicking an effective turbulent viscosity in the early phases of the rings evolutions.