Jazz pianist's arrangement of Waterfalls (4,6)
I believe the answer is:
fats waller
'jazz pianist's' is the definition.
(Fats Waller, US pianist 1904-1943)
'arrangement of waterfalls' is the wordplay.
'arrangement of' is an anagram indicator.
'waterfalls' is an anagram of 'FATS WALLER'.
(Other definitions for fats waller that I've seen before include "Jazzman" , "American jazz musician, d. 1943" .)