Palaver to fix Cockney's cavity following damage (9)
I believe the answer is:
rigmarole
'palaver' is the definition.
(both can mean a complicated process)
'fix cockney's cavity following damage' is the wordplay.
'fix' becomes 'rig' (rigging is a kind of fixing).
'cockney's cavity' becomes ''ole' ('hole' - hole is a kind of cavity - said with the 'H' dropped - a cockney accent.).
'following' is a charade indicator (letters next to each other).
'damage' becomes 'mar' (to mar is to spoil or damage).
'ole' put after 'mar' is 'marole'.
'rig'+'marole'='RIGMAROLE'
'to' is the link.
(Other definitions for rigmarole that I've seen before include "Long, rambling story" , "Palaver" , "Long, rambling statement or complicated procedure" , "red tape?" , "Long, complicated and confusing procedure" .)