Exhale audibly (4)
I believe the answer is:
'exhale audibly' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for sigh that I've seen before include "expire, sadly" , "Weary sound" , "Audible exhalation of breath" , "Utterance made by exhaling audibly" , "Moan softly" .)