Pesek was born in Prague and studied conducting, piano, cello and trombone at the Academy of Musical Arts there, Vaclav Smetacek and Karel Ancerl among his teachers. He worked at the Pilsen and Prague Operas, and from 1958 to 1964 was the founder director of Prague Chamber Harmony. He was chief conductor of the Slovak Philharmonic Orchestra in 1980-81, and from 1982 to 1990 was conductor in residence of the Czech Philharmonic Orchestra. He was music director of the Royal Liverpool Philharmonic Orchestra from 1987 to 1998, becoming conductor laureate thereafter. He has guest conducted a large number of other orchestras.
Pesek is best known for his interpretations of Czech music. He has been a champion lesser known Czech composers, particularly Josef Suk and Vitezslav Novák.