Evelyn distributed smoothly (6)
I believe the answer is:
evenly
'smoothly' is the definition.
(thesaurus)
'evelyn distributed' is the wordplay.
'distributed' indicates an anagram.
'evelyn' is an anagram of 'EVENLY'.
(Other definitions for evenly that I've seen before include "Smoothly or fairly" , "impartial manner" , "In equal proportion" , "In measured or smooth manner" , "In measured manner or fairly" .)