At a very young age, he learned to play the clarinet from his father, also a clarinetist, and later studied at the Hochschule für Musik in Berlin.

As a teenager, he was accepted into the Komische Oper Berlin under Václav Neumann and Walter Felsenstein as clarinet soloist.

In 1959, Leister joined the Berlin Philharmonic Orchestra under the baton of Herbert von Karajan;[1] this musical association was to last for thirty years.

The creation of the Herbert von Karajan Academy of the Berlin Philharmonic Orchestra has permitted Leister to teach music to a whole new generation of musicians.

From 1993 to 2002, Leister held the position of Professor at the Hochschule für Musik "Hanns Eisler" in Berlin.