Greer played with the band by Elmer Snowdenen the binding of the Howard Theatre in Washington, D.C.. In 1919 he met Duke Ellington. From 1923 he would be part of Ellington's Orchestra, when vijfmansgroep, a Ellington's Washingtonians. Greer would be Ellington drummer until 1951, where he cut a dash in addition to his drum kit made by a range of other shiny (percussion) instruments and play (a gong, tubular bells, a timpani and xylophone). He also hoped to impress the women. Greer would eventually marry a dancer of the Cotton Club.
Greer was one of the first drummers who in addition to his drum also other percussion instruments played. His game was tasteful and subtle and paste at the sound that Ellington wanted. He played relaxed, but that wild may cause he loved not the size. With bassist Jimmy Blanton , he formed one of the most strongest rhythm sections ever.On several songs in the 1920s and 1930s is Greer also as a singer to hear.
In the 1930s and 1940s he played a few times with other orchestras, including that of Lionel Hampton (during one of his famous Victor-sessions).
Greer had a drinking problem and was therefore not entirely reliable. When Ellington for a tour of Scandinavia for the Security took an additional drummer and Greer are appealed, there was disagreement on drink and left Greer the band. He continued with the new group of Johnny Hodges, also a veteran of Ellington's Orchestra. The contact with Ellington was never broken. Greer worked freelance with Henry ' Red ' Allen, Tyree Glenn and J.C. Higginbottham. During the late 1960s and 1970s, he had a private group, usually a trio. In the 1970s there were several Ellington tribute performances, where he sat behind the drums.