Cold shoulder and rolls sent back (4)
I believe the answer is:
snub
'cold shoulder' is the definition.
('snub' can be a synonym of 'cold shoulder')
'rolls sent back' is the wordplay.
'rolls' becomes 'buns' ('bun' can be a synonym of 'roll').
'sent back' shows that the letters should be reversed in order.
'buns' written backwards gives 'SNUB'.
'and' acts as a link.
(Other definitions for snub that I've seen before include "Give (someone) the cold shoulder" , "Ignore, spurn disdainfully" , "Check" , "Rebuff or reject someone" , "16" .)