Inspector Lewis's first piece (6)
I believe the answer is:
morsel
'piece' is the definition.
(I have seen 'Small piece' mean 'morsel' so perhaps 'piece' could also mean 'morsel')
'inspector lewis's first' is the wordplay.
'inspector' becomes 'morse' (Inspector Morse).
'lewis's first' becomes 'l' (1st letter of 'lewis').
'morse'+'l'='MORSEL'
(Other definitions for morsel that I've seen before include "Crumb" , "a little food" , "Small amount of food, a bite" , "Dainty" , "A tiny bit" .)