Lucky dip bishop operated -- only on the counter (4,3)
I believe the answer is:
bran tub
'lucky dip' is the definition.
(I've seen this before)
'bishop operated only on the counter' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'operated' becomes 'ran' ('run' can be a synonym of 'operate').
'only' becomes 'but' (but can mean only - eg 'life is but a dream').
'on the counter' shows that the letters should be reversed in order (counter can mean in the opposite direction).
'but' reversed gives 'tub'.
'b'+'ran'+'tub'='BRAN-TUB'
(Other definitions for bran tub that I've seen before include "Lucky-dip container" , "Container for lucky dip" , "Gifts from here" , "place for a dip" .)