A composite seal structure adapted to be mounted in a turbomachine, the composite seal structure comprising: a carrier ring having: a circumferential outer wall (33.1) with an inner surface and an outer surface, a first side wall (33.2), and a second side wall (33.3), wherein the first side wall and the second side wall protrude radially inwardly from the circumferential outer wall towards an axis of the carrier ring; wherein an annular groove (33.4) is formed between the circumferential outer wall (33.1), the first side wall (33.2) and the second side wall (33.3); a seal element having a first region (35.2) in surface-to-surface contact with the annular groove (33.4) and a second, sealing region (35.12) protruding from the annular groove of the carrier ring toward the axis of the carrier ring and provided with sealing features (35.5); and a fastening arrangement coupling the seal element and the carrier ring to one another forming said composite seal structure; wherein the fastening arrangement comprises a plurality of fastening pins (37, 39) circumferentially arranged around the axis of the carrier ring; wherein each fastening pin of the plurality of fastening pins extends through at least one of the first side wall (33.2) and second side wall (33.3); and wherein each fastening pin of the plurality of fastening pins (37, 39) engages in a corresponding seat (35.10, 35.11) formed in the seal element; characterized in that the plurality of fastening pins comprise: a first set of fastening pins extending through holes (33.7) across the first side wall (33.2) and engaging into a first set of the seats (35.10) of the seal element; and a second set of fastening pins extending through holes (33.8) across the second side wall (33.3) and engaging into a second set of the seats (35.11) of the seal element; and wherein the seats (35.10, 35.11) are in the shape of blind holes in the seal element. a carrier ring having: a circumferential outer wall (33.1) with an inner surface and an outer surface, a first side wall (33.2), and a second side wall (33.3), wherein the first side wall and the second side wall protrude radially inwardly from the circumferential outer wall towards an axis of the carrier ring; wherein an annular groove (33.4) is formed between the circumferential outer wall (33.1), the first side wall (33.2) and the second side wall (33.3); a seal element having a first region (35.2) in surface-to-surface contact with the annular groove (33.4) and a second, sealing region (35.12) protruding from the annular groove of the carrier ring toward the axis of the carrier ring and provided with sealing features (35.5); and a fastening arrangement coupling the seal element and the carrier ring to one another forming said composite seal structure; wherein the fastening arrangement comprises a plurality of fastening pins (37, 39) circumferentially arranged around the axis of the carrier ring; wherein each fastening pin of the plurality of fastening pins extends through at least one of the first side wall (33.2) and second side wall (33.3); and wherein each fastening pin of the plurality of fastening pins (37, 39) engages in a corresponding seat (35.10, 35.11) formed in the seal element; characterized in that the plurality of fastening pins comprise: a first set of fastening pins extending through holes (33.7) across the first side wall (33.2) and engaging into a first set of the seats (35.10) of the seal element; and a second set of fastening pins extending through holes (33.8) across the second side wall (33.3) and engaging into a second set of the seats (35.11) of the seal element; and wherein the seats (35.10, 35.11) are in the shape of blind holes in the seal element.