Admirer of Cockney’s home listened to (4)
I believe the answer is:
beau
'admirer' is the definition.
(I've seen this before)
'cockney's home listened to' is the wordplay.
'cockney's home' becomes 'bow' (area of East London).
'listened to' shows a homophone (sound like).
'bow' is a homophone of 'BEAU'.
'of' acts as a link.
(Other definitions for beau that I've seen before include "Admirer; fop, dandy" , "Male suitor - dandy" , "An old-fashioned boy friend (4)" , "Dandy - boyfriend" , "An old-fashioned boy friend - like Brummel?" .)