Pretend not to have seen Annie belt Rudy viciously (4,1,5,3)
I believe the answer is:
turn a blind eye
'pretend not to have seen' is the definition.
(I've seen this before)
'annie belt rudy viciously' is the wordplay.
'viciously' indicates anagramming the letters.
'annie'+'belt'+'rudy'='anniebeltrudy'
'anniebeltrudy' anagrammed gives 'TURN A BLIND EYE'.
(Other definitions for turn a blind eye that I've seen before include "Affect not to see" , "Ignore -- brush aside" , "Overlook deliberately" , "Follow Nelson's example" , "pay no attention" .)