[2] She studied at the Juilliard School with Leonard Rose and Lynn Harrell,[2] and performed in the masterclasses of Mstislav Rostropovich.
[3] After receiving a Rockefeller grant to study in London, England with Jacqueline du Pré,[3] she continued her studies at the Robert Schumann Hochschule in Düsseldorf, Germany with Johannes Goritzki.
[4][better source needed] Green was the first cellist to record the complete Hungarian Dances of Brahms arranged by Alfredo Piatti, Franz Schmidt’s Three Fantasy Pieces (after Hungarian National Melodies), and the complete works of Mario Castelnuovo-Tedesco, all on Biddulph Recordings (London, UK) and later re-issued on JRI Recordings (USA).
Other premieres include Donald Francis Tovey's sonata for solo cello (JRI), the complete works for cello and piano of Robert Fuchs (Biddulph), complete Arensky works for cello[5][better source needed] (JRI) and works of Venezuelan composer Paul Desenne (Cello Classics) as well as Mendelssohn-Merk Variations in A major, newly completed by R. Larry Todd and published by Bärenreiter (JRI).
With her longstanding duo partner, Frederick Moyer, (also her cousin), Green recorded numerous CDs on the JRI label.