An implant for heart valve repair, the implant comprising: a clamp movable between an open position and a closed position in which the clamp is able to grasp a leaflet of a heart valve, so as to fix the implant on the leaflet; and a shutter comprising a structure adapted to pass automatically from a contracted configuration to an expanded configuration in which 5 the shutter is able to fill at least partially an opening portion remaining between the leaflet and at least one further leaflet of the heart valve of the heart valve, when the implant is attached to one leaflet, so as to limit a backflow of blood through the opening portion when the heart valve closes, and wherein the structure is curved in two directions perpendicular to each other in the expanded configuration.