A turbine ring assembly comprising a plurality of ring sectors made of ceramic-matrix composite material forming a turbine ring and a ring support structure, each ring sector having, along a cutting plane defined by an axial direction (D A) and a radial direction (D R) of the turbine ring, said axial direction corresponding to the direction of flow of a gas stream in said turbine, a base with, in the radial direction (D R) of the turbine ring, a radially inner face defining the inner face of the turbine ring and a radially outer face from which an upstream attachment lug and a downstream attachment lug protrude, said ring support structure including a shroud which extends around the turbine ring, from which an upstream radial clamp and a downstream radial clamp by which the upstream and downstream attachment lugs (14, 16) of each ring sector are held radially protrude towards the turbine ring, said shroud including, relative to said direction of flow of a gas stream in said turbine: a first upstream portion which extends radially above the first attachment lug and a second downstream portion which extends in the extension of the first upstream portion and radially above the second attachment lug, said first upstream portion having the shape of a right cylinder and the second downstream portion having a frustoconical shape which, from one end of the first upstream portion, extends towards the axis of the turbine ring while having a generally constant thickness; said upstream radial clamp extending from said upstream portion to bear, directly or indirectly, against the upstream attachment lug, while the downstream radial clamp extends from the downstream portion to come into contact against the downstream attachment lug, characterized in that the ring is held, relative to said radial clamps (32, 36), by axial pins (119, 120) which cooperate respectively on the one hand with the upstream radial clamp, via first and second annular flanges (33, 34) and directly with the downstream radial clamp, and on the other hand, with the upstream and downstream attachment lugs (14, 16). a first upstream portion which extends radially above the first attachment lug and a second downstream portion which extends in the extension of the first upstream portion and radially above the second attachment lug, said first upstream portion having the shape of a right cylinder and the second downstream portion having a frustoconical shape which, from one end of the first upstream portion, extends towards the axis of the turbine ring while having a generally constant thickness; said upstream radial clamp extending from said upstream portion to bear, directly or indirectly, against the upstream attachment lug, while the downstream radial clamp extends from the downstream portion to come into contact against the downstream attachment lug, characterized in that the ring is held, relative to said radial clamps (32, 36), by axial pins (119, 120) which cooperate respectively on the one hand with the upstream radial clamp, via first and second annular flanges (33, 34) and directly with the downstream radial clamp, and on the other hand, with the upstream and downstream attachment lugs (14, 16).