Impingement insert for an airfoil of a blade/vane of a gas turbine is provided. The impingement insert includes a double-walled section having an outer and an inner walls, that define—an inner channel at an inner surface of the inner wall, an outer channel at an outer surface of the outer wall and a middle channel between the outer and the inner walls. Impingement cooling holes are provided in the outer wall that use the cooling air of the middle channel to eject impingement jets into the outer channel. The impingement insert includes at least one extraction duct that extends between the outer and the inner walls across the middle channel, and has an inlet at the outer channel, and an outlet at the inner channel, for flowing the cooling air, after impingement, from the outer channel into the inner channel.