Once-healthy duke blew out (7)
I believe the answer is:
exhaled
'blew out' is the definition.
(I've seen this in another clue)
'once-healthy duke' is the wordplay.
'once' becomes 'ex' (prefix meaning former or onetime).
'healthy' becomes 'hale' (hale can mean fit and healthy).
'duke' becomes 'd' (abbreviation).
'ex'+'hale'+'d'='EXHALED'
(Other definitions for exhaled that I've seen before include "Breathed out" , "Gave off" , "Sent out" , "blown out" .)