Drowsy, left the cigar to go out (9)
I believe the answer is:
lethargic
'drowsy' is the definition.
(thesaurus)
'left the cigar to go out' is the wordplay.
'left' becomes 'l' (common abbreviation).
'to go out' indicates an anagram.
'the'+'cigar'='thecigar'
'thecigar' is an anagram of 'ethargic'.
'l'+'ethargic'='LETHARGIC'
(Other definitions for lethargic that I've seen before include "Lacking in energy or vitality" , "Lackadaisical" , "Enervated" , "lack of energy" , "Sluggish and apathetic" .)