The composite seal structure includes a carrier ring and a seal element housed in an annular groove formed between a circumferential outer wall and two side walls of the carrier ring. The seal element has a first region in surface-to-surface contact with the annular groove and a second, seal-ing region protruding from the annular groove. A fastening arrangement couples the seal element and the carrier ring to one another. The fastening arrangement comprises a plurality of fastening pins circumferentially arranged around the axis of the carrier ring. Also disclosed is a method for manufacturing the seal structure.