Deliberately ignore the alternative method after search (4,3,5,3)
I believe the answer is:
look the other way
'deliberately ignore' is the definition.
'the alternative method after search' is the wordplay.
'alternative' becomes 'other' (I've seen this before).
'method' becomes 'way' (I've seen this before).
'after' means one lot of letters go next to another.
'search' becomes 'look' ('look' can be a synonym of 'search'**).
'the'+'other'+'way'='theotherway'
'theotherway' after 'look' is 'LOOK THE OTHER WAY'.
(Other definitions for look the other way that I've seen before include "turn a blind eye" , "have alternative appearance?" , "Wink at something" , "Take no notice" .)