Sloth disturbed a composer (5)
I believe the answer is:
holst
'a composer' is the definition.
(Gustav Holst)
'sloth disturbed' is the wordplay.
'disturbed' is an anagram indicator (the order of letters is disturbed).
'sloth' with letters rearranged gives 'HOLST'.
(Other definitions for holst that I've seen before include "He scored" , "Scorer" , "musical writer" , "British composer, 1874-1934" , "Gustav --, English composer" .)