Handouts earl distributes with complete sincerity (5,3,4)
I believe the answer is:
heart and soul
'with complete sincerity' is the definition.
(I've seen this before)
'handouts earl distributes' is the wordplay.
'distributes' is an anagram indicator (I've seen 'distributing' mean this).
'handouts'+'earl'='handoutsearl'
'handoutsearl' is an anagram of 'HEART AND SOUL'.
(Other definitions for heart and soul that I've seen before include "With complete devotion" , "With complete sincerity" .)