Dropping trousers, rector showing member (4)
I believe the answer is:
part
'member' is the definition.
(e.g. member of the family is part of the family)
'dropping trousers rector' is the wordplay.
'dropping' becomes 'pat' (eg a cow pat).
'trousers' indicates putting letters inside (to trouser can mean to contain or hold).
'rector' becomes 'r'.
'pat' placed around 'r' is 'PART'.
'showing' is the link.
(Other definitions for part that I've seen before include "Component; divide" , "Some - theatrical role" , "Separate - role" , "Constituent - something to play?" , "Piece, segment" .)