Rebuff, ignore (4)
I believe the answer is:
snub
This clue is a double definition.
'rebuff' is the first definition.
(snub is a kind of rebuff)
'ignore' is the second definition.
(synonyms)
(Other definitions for snub that I've seen before include "Ignore totally" , "unusually short" , "Rude put-down; blunt (nose)" , "Ignore, spurn disdainfully" , "Cold-shoulder" .)