Say goodbye to a role (4)
I believe the answer is:
part
I believe this is a double definition.
'say goodbye' is the first definition.
(I've seen this in another clue)
'role' is the second definition.
(eg a part or role in a film)
'to a' acts as a link.
(Other definitions for part that I've seen before include "Piece, segment" , "Some - theatrical role" , "Divide; role" , "Section of a whole" , "Element" .)