Elisabeth Klein was born in Trenčín (now Slovakia) and grew up in Budapest, Hungary from the age of 3. At an early age, she showed interest and talent for the piano. She studied at the Franz Liszt Academy already as a young girl, continuing after high school, graduating from the Academy in 1934, where-after she studied privately with Béla Bartók 1934–1936. She formed a duo with the violinist László Halmos. The political turmoil in the thirties made many musicians, not least Jews, leave Budapest. EK came to Denmark without clear plans, however, to stay, but at the outbreak of the Second World War she managed to stay. She met her later husband Jørgen Petersen (1916–1986), a Royal Danish Naval Officer, and they married on December 21, 1941. Their first son, Ole Holger, was born in 1943. During the last years of the war, Jørgen was exiled in Scotland, and after his return, their second son, Nils Holger, was born in 1946. The family spent some years stationed with N.A.T.O. in Oslo, Norway, and in Kiel, West Germany, 1956–59. Elisabeth Klein worked for many years with the Royal Danish Opera in Copenhagen, later she taught at the Royal Danish Academy of Music in Copenhagen, Denmark, and at the Norwegian Academy of Music, Oslo, Norway. Again, from 1969–71, she and her husband lived in Oslo, and even after they moved back to Copenhagen, she continued commuting between her two teaching positions in Copenhagen and Oslo, until, in 1980, at her husband’s retirement, they moved to Oslo again, and she stopped teaching in Copenhagen. She continued her engagement with the Academy of Music in Oslo. After her own retirement from the Academy in 1981, she continued giving seminars and lecture-recitals at the Academy for many years.
Her interest in contemporary music had been sparked by her studies with Béla Bartók, whose piano music she performed extensively in Denmark and later in many other countries. In the 1960s, this led to a new focus on music written after the Second World War, not least the music of Pierre Boulez and Karlheinz Stockhausen, and she became a particular champion of and specialist in the performance of Contemporary Scandinavian piano music. She also did much to promote women composers, participating, e.g. in International Congresses on Women in Music. She performed concerts and made numerous recordings throughout the Nordic countries and altogether in (Western) Europe, the U.S., Israel, Mexico, and China. Her discography includes works by Bartók, Schoenberg, Berg, Webern, Stockhausen and many contemporary Scandinavian composers. Many piano works were specifically written and also dedicated to her by various composers. In 1999, she moved to Liverpool, UK; and spend her final years living with her oldest son and his family, still actively performing and teaching the piano, not least and numerous lecture-recitals at the Music Department at Liverpool University. Elisabeth Klein was awarded the Music Prize of Danish Radio in 1966, made an honorary artist of the Norwegian Composers Association in 1976, and became an honorary member of Women in Music in 1992.