Small part of Society? Of course (6)
I believe the answer is:
snatch
'small part' is the definition.
(snatch can mean a small bit of something)
'society? of course' is the wordplay.
'society?' becomes 's' (common abbreviation in names of organisations).
'of course' becomes 'natch' (short for 'naturally').
's'+'natch'='SNATCH'
'of' acts as a link.
(Other definitions for snatch that I've seen before include "American kidnapping" , "Seize suddenly" , "Grab suddenly" , "heist" , "pull" .)