A turbine nozzle sector that comprises an outer platform segment and an inner platform segment between which there extend one or more hollow vanes. Each vane presents a trailing edge cavity for feeding with cooling air and communicating with a plurality of vents distributed along the trailing edge of the vane, these vents serving to exhaust a fraction of the cooling air. Said cavity communicates with an air outlet hole situated level with the outer platform and enabling a fraction of the cooling air to be exhausted.