Leonard studied at Brooklyn College. In 1949 he obtained Bachelor of Laws degree, graduating from Brooklyn Law School.
Leonard started his career at Mudge Rose Guthrie Alexander & Ferdon law firm in New York, United States in 1946 and worked there till 1969, when he was appointed a special counsel to the United States President Richard M. Nixon, a post he held till 1973. The same year he started to serve as an acting counsel. He held this position till 1974.
In 1973 Garment started to work as a vice chair at the Administrative Conference of the United States and held the position till 1974, when he became an assistant to United States President Gerald R. Ford.
One year later, Leonard served as a United States representative at the United Nations Commission on Human Rights.
As the 1980s drew to a close, he worked with John Brandemas as co-chair of an independent commission investigating the National Endowment for the Arts.
Leonard also served as the United States Ambassador to the Third Committee at the United Nations.
Garment had a long association with the arts and was a chairman of the board of the Brooklyn Academy of Music in the 1970s.
Leonard Garment was a member of New York Bar Association, District of Columbia Bar Association and American Bar Association.
Leonard married Grace Albert Garment, a writer, on June 20, 1951. In 1976 the woman died. The couple had three children: Ann Rebecca, Sara and Paul.
Suzanne Rose Weaver became the second wife of Leonard on January 1, 1980.