He played junior hockey for the Galt Black Hawks and the Barrie Flyers from 1954 to 1956. He then turned pro for the Boston Bruins in 1956-57, as well as playing for the Quebec Aces and the Victoria Cougars.
Beckett played mostly in the minor pros but had three more stints with the Bruins in 1957-58, 1961-62, and 1963-64. In total he played 68 NHL games (all with the Bruins) and scored 7 goals and 6 assists. He retired in 1964.