Pay no attention to Italian chap down south (6)
I believe the answer is:
ignore
'pay no attention' is the definition.
(I've seen this before)
'italian chap down south' is the wordplay.
'italian chap' becomes 'signore' (Italian equivalent to 'mister').
'down' indicates named letters should be taken away ('down' can mean missing).
'south' becomes 's' ('S' can be a synonym of 'south').
'signore' with 's' removed is 'IGNORE'.
'to' acts as a link.
(Other definitions for ignore that I've seen before include "Brush off" , "Pay no heed to" , "Refuse to notice or acknowledge" , "Deliberately take no notice" , "Fail to observe" .)