Paul Kleber was born in Berlin (Germany) and started playing cello and drums before he chose his main instrument, the double bass. He studied classical music at the Hanns Eisler School of Music Berlin and later jazz at the Universität der Künste Berlin. He recorded and played live with Jazzanova, Sebastian Studnitzky, Fink, Micatone, Nylon, JazzIndeed and Lisa Bassenge.
As a sideman he accompanied many artists i.e. Dee Dee Bridgewater, Mark Murphy, Emiliana Torrini, Nina Hagen, Nils Landgren, David Friedman and Nightmares On Wax.