Affair of the bag (4)
I believe the answer is:
case
I believe this clue is a double definition.
'affair' is the first definition.
'the bag' is the second definition.
(I have seen 'Overnight bag' mean 'case' so perhaps 'bag' could also mean 'case')
'of' acts as a link.
(Other definitions for case that I've seen before include "Humorous character" , "Cover" , "Piece of luggage and a lawyer's proceeding" , "Box or outer covering" , "Check out" .)