Beckett studies organ with George Hewson and harmony with John Francis Larchet at the Royal Irish Academy of Music (RIAM), in addition to music at Trinity College Dublin where he is conferred with a Mus.D. (Doctor of Music) in 1942. He lives from 1946 to 1963 in Venice, where he teaches English and piano. He also writes reviews from abroad for The Irish Times and makes a series of orchestral arrangements of Irish traditional music for Radio Éireann.
In addition to Beckett’s activity as a music critic for The Irish Times, he also writes biographical articles for dictionaries, in particular for the first edition of Die Musik in Geschichte und Gegenwart. His books include studies on Franz Liszt and ballet music.
Beckett’s more ambitious musical works from the 1940s and 1950s are a Suite for Orchestra (1945), Four Higgins Songs (1946), The Falaingin Dances (1958) and a Suite of Planxties (1960) for harp and orchestra.
In 1963 Beckett moves to England, where he teaches music at various schools before returning to Ireland in 1970 to succeed A. J. Potter at the RIAM as professor of harmony and counterpoint. In the 1980s he produces a number of remarkable works such as Quartet for Strings (1980) and Dublin Symphony (1989) for narrator, chamber choir and large orchestra. While he is never a modernist, his later works nevertheless contain some advanced harmony, particularly in the quartet.