Shun Italian man denied introduction (6)
I believe the answer is:
ignore
'shun' is the definition.
'italian man denied introduction' is the wordplay.
'italian man' becomes 'signore'.
'denied introduction' means to remove the first letter.
'signore' with its first letter taken away is 'IGNORE'.
(Other definitions for ignore that I've seen before include "Walk away from" , "Turn a blind eye to" , "Spurn" , "Fail to consider" , "Discount" .)