Those with mates passed around note giving periods of opportunity (7)
I believe the answer is:
windows
'periods of opportunity' is the definition.
(windows of opportunity)
'those with mates passed around note' is the wordplay.
'those with mates passed' becomes 'widows' (a widow's spouse has passed away).
'around' indicates putting letters inside.
'note' becomes 'n' (abbreviation).
'widows' placed around 'n' is 'WINDOWS'.
'giving' is the link.
(Other definitions for windows that I've seen before include "Microsoft operating system" , "openings" , "Computer operating system with a graphical user interface" .)