Old copper has piano from East Enders sweetheart's scratched (4)
I believe the answer is:
anna
'old copper' is the definition.
(old copper coin)
'piano from east enders sweetheart's scratched' is the wordplay.
'piano from east enders' becomes 'Joanna' (Joanna is Cockney rhyming slang for piano).
'sweetheart' becomes 'jo' (Scottish term for darling or sweetheart).
'scratched' suggests deleting specific letters (scratch can mean to remove or delete).
'joanna' with 'jo' removed is 'ANNA'.
'has' acts as a link.
(Other definitions for anna that I've seen before include "Massey, Sewell or Karenina" , "Old Indian coin - girl's name" , "Former one sixteenth of Rupee" , "Unit of length" , "She's a woman, whichever way you look at it" .)