Ignore tiny, endurable failing (4,1,5,3)
I believe the answer is:
turn a blind eye
'ignore' is the definition.
(I've seen this before)
'tiny endurable failing' is the wordplay.
'failing' indicates an anagram.
'tiny'+'endurable'='tinyendurable'
'tinyendurable' anagrammed gives 'TURN A BLIND EYE'.
(Other definitions for turn a blind eye that I've seen before include "Overlook deliberately" , "Refuse to acknowledge" , "take no notice" , "Pretend not to notice" , "pay no attention" .)