Perfume, we hear, that's dispatched (4)
I believe the answer is:
sent
'dispatched' is the definition.
(I've seen this in another clue)
'perfume we hear' is the wordplay.
'perfume' becomes 'scent' (synonyms).
'we hear' shows a homophone (sound like).
'scent' is a homophone of 'SENT'.
'that's' acts as a link.
(Other definitions for sent that I've seen before include "Remitted" , "Transmitted" , "Thrilled" , "Transported" , "Caused to go somewhere" .)