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