In the 1960s Jiří Daler was one of the best track cyclists from Czechoslovakia, winning gold at the Olympics and five medals at the UCI World Championships. Daler made his début at the World Road Championships in 1962, finishing ninth in the 100 kilometres team time trial. After riding some further amateur road races, he became a track specialist, earning himself a place on the Olympic team for the 1964 Tokyo Games. The hard work paid off with Daler winning gold in the 4,000 metres individual pursuit, beating Giorgio Ursi (ITA) in the final. A few days later he also placed fifth in the 4,000 metres team pursuit with his compatriots before also racing in the individual road race. That year Daler also won bronze in the individual pursuit at the track world championships in Paris.
Daler continued to focus on his track career, winning bronze in the team pursuit at the 1965 track world championships. The following year he won silver in the individual pursuit and bronze in the team event, before winning an individual bronze in 1967. One year later he returned to the Olympics, competing in the velodrome at the 1968 Mexico City Games. He failed, however, to repeat his previous success at the Games when he was eliminated in the qualifying round of the individual pursuit. In the late 1960s Daler competed in road races, riding in stage races and one-day races in France. After his professional career ended he returned to Czechoslovakia where he worked as an electrical engineer.