Despite the shelving of his first session, Green's recording relationship with Blue Note was to last, with a few exceptions, throughout the 1960s. From 1961 to 1965, Green made more appearances on Blue Note LPs, as leader or sideman, than anyone else. Green's first issued album as a leader was "Grant's First Stand". This was followed in the same year by "Green Street" and "Grantstand". Grant was named best new star in the "Down Beat" critics' poll, in 1962. He often provided support to the other important musicians on Blue Note, including saxophonists Hank Mobley, Ike Quebec, Stanley Turrentine and organist Larry Young.