Snub Italian gentleman lacking introduction (6)
I believe the answer is:
ignore
'snub' is the definition.
(snub can mean to ignore)
'italian gentleman lacking introduction' is the wordplay.
'italian gentleman' becomes 'signore' (Italian equivalent to mister).
'lacking introduction' means to remove the first letter.
'signore' with its initial letter removed is 'IGNORE'.
(Other definitions for ignore that I've seen before include "Fail to observe" , "bypass" , "Neglect" , "Give no attention to" , "Brush off" .)