Hank is the oldest brother of the Jones jazz family (the others are Thad and Elvin). In 1944 he went to New York and first played with Hot Lips Page, followed by Coleman Hawkins, Billy Eckstine, Howard McGhee and Andy Kirk and. In the 1950s he played with Lester Young, Cannonball Adderley, Artie Shaw and Benny Goodman and many others. He was a CBS studio musician during the 60's and 70's, but kept played jazz.