Record Cockney firm making scrap (7)
I believe the answer is:
discard
'scrap' is the definition.
(scrap can mean to discard)
'record cockney firm' is the wordplay.
'record' becomes 'disc' (eg a CD, compact disc).
'cockney firm' becomes ''ard' ('hard' - both can mean durable or strong - said with the 'H' dropped - a cockney accent.).
'disc'+'ard'='DISCARD'
'making' is the link.
(Other definitions for discard that I've seen before include "Throw away or cast off" , "Jettison" , "bin" , "Abandon" , "Shed" .)