An implant for improving coaptation of an atrioventricular valve, the atrioventricular valve having a native first leaflet, a native second leaflet and an annulus and controlling blood flow from an upstream side to a downstream side of the valve, the implant comprising a support structure configured to be fixed to the annulus or to the native first leaflet, the implant further comprising a flexible artificial leaflet structure mounted to the support structure and comprising a rim section that is shaped to coapt with the native second leaflet, wherein said rim section comprises pockets that are open towards said downstream side and capable of being filled with blood from the downstream side each time the valve is closed.