The invention relates to a turbine assembly comprising: a plurality of ring sectors forming a ring; a support structure comprising a shroud from which there project radial flanges which serve to hold latching tabs of each ring sector; a stator positioned downstream of said ring and comprising a blade provided with a radially outer platform and extending axially opposite said ring; an annular space being defined between the ring, the support structure and the platform, this annular space having passing through it a leakage air current, the assembly comprising a hollow ring which occupies said annular space and which is shaped so as to collect, channel and expel said leakage air current, more specifically to channel and expel it into the radially inner region of said annular space.