A gas turbine with a stator blade is disclosed. The stator blade is fastened on a blade carrier and includes a blade airfoil which extends inwards in the radial direction from an outer platform into a hot gas passage. A cooling medium can flow through an interior of the blade airfoil, such as cooling air, which flows through an access in the blade carrier into a first plenum which is arranged above the outer platform, and from there, via an inlet which is provided in the outer platform, flows into the interior of the blade airfoil.