Affair of the bag (4)
I believe the answer is:
case
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' is the 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" .)