Not much of a part (3)
I believe the answer is:
bit
I believe this clue is a double definition.
'not much' is the first definition.
'a part' is the second definition.
(both mean a piece of something)
'of' acts as a link.
(Other definitions for bit that I've seen before include "'Part, fragment (3)'" , "Cutting head of a drill" , "Small piece; boring tool" , "Unspoken" , "chip?" .)