Pešek was born in 1933 in Prague into a non-musical family. His mother encouraged his musical interests from a young age and arranged for him to have piano lessons. As a teenager he formed a jazz band with his friends from school, and he continued studying classical music in his piano lessons. Later, he attended the Academy of Musical Arts in Prague, where he studied with Karel Ancerl and Václav Smetácek. However, Pešek admitted that he was largely self-taught because his professors rarely showed up to the lessons. He also learned both the cello and trombone because he thought it was important for a conductor to experience the orchestra from different perspectives. While still a student, he worked as a rehearsal director at the Plzen ballet company and then the Prague National Theater. After he graduated, he founded and conducted the Prague Chamber Harmony wind ensemble, and he also conducted the Sebastian Orchestra in Prague. With these ensembles, Pešek's reputation as a conductor quickly grew, which led to appointments with more prominent orchestras. He conducted the Czech Chamber Orchestra from 1970 to 1977, and he also worked with the Frysk Orkester in the Netherlands. Beginning in 1980, he conducted the Slovak Philharmonic Orchestra for two seasons, and then he served as the conductor-in-residence for the Czech Philharmonic Orchestra in 1982. From then until 1990, he kept conducting the Czech PO, and performed several tours in Japan, North America, and Europe.
In 1987 Pešek began a ten-year appointment as principal conductor for the Royal Liverpool Philharmonic Orchestra, and he remained associated with the Czech PO as its principal guest conductor. He brought the RLPO international acclaim after their tour to the United States in 1992, and the corresponding series of recordings. His time in Liverpool was also a period of transformation as he quit smoking, became a vegetarian, and started practicing Buddhism. Feeling the need to reduce his professional obligations, he stepped down from his position with the RLPO in 1997 and became a lifetime conductor laureate. Pešek continued performing in a reduced capacity, and he became the chief conductor of the Czech National Symphony Orchestra in 2007. He made his final appearance with the RLPO in 2013 in a concert celebrating his 80th birthday. Pešek retired in 2019 and spent his final years enjoying nature and his beloved pet dogs. He passed away in a hospital in Prague on October 23, 2022, at 89 years old. ~ RJ Lambert, Rovi