Inspector silent eating singular Chinese appetiser (3,3)
I believe the answer is:
dim sum
'chinese appetiser' is the definition.
(I've seen this before)
'inspector silent eating singular' is the wordplay.
'inspector' becomes 'di' (abbreviation for Detective Inspector).
'silent' becomes 'mum' (keep mum).
'eating' indicates putting letters inside.
'singular' becomes 's' (abbreviation sometimes used in dictionaries).
'mum' enclosing 's' is 'msum'.
'di'+'msum'='DIM SUM'
(Other definitions for dim sum that I've seen before include "fare from China" , "Chinese dish, includes dumplings" , "Chinese dumpling dish" , "Chinese fare" , "starters?" .)