Starter of fish and chips cooked in oil originally (9)
I believe the answer is:
carpaccio
'starter' is the definition.
(I've seen this before)
'fish and chips cooked in oil originally' is the wordplay.
'fish' becomes 'carp' (carp is a kind of fish).
'originally' suggests taking the first letters.
The initial letters of 'and chips cooked in oil' is 'accio'.
'carp'+'accio'='CARPACCIO'
'of' is the link.
(Other definitions for carpaccio that I've seen before include "Italian framed" , "Italian ham" , "Starter" , "Italian hors d'oeuvre" , "Thin slices of raw meat or fish" .)