Triggering Discoveries in High Energy Physics III will take place in High Tatras, Slovakia, between December 9 th and December 13th of 2024. It will be hosted by the Institute of Physics of the Pavol Jozef Šafárik University in Košice. The purpose of this workshop is to discuss the role of triggering in enabling studies in high energy physics and astroparticle physics experiments, and in discussing the latest developments in the technical execution of triggers. The conference will be held at Atrium Hotel (Nový Smokovec). The conference covers both theory and experiment/observations in most