Test: most ending in failure rejected (4)
I believe the answer is:
exam
'test' is the definition.
('exam' can be a synonym of 'test')
'most ending in failure rejected' is the wordplay.
'most' becomes 'max' (maximum).
'ending in' says to take the final letters.
'rejected' is a reversal indicator.
The last letter of 'failure' is 'e'.
'max'+'e'='maxe'
'maxe' written backwards gives 'EXAM'.
(Other definitions for exam that I've seen before include "Test (abbr)" , "Important test" , "One test" , "Written test" , "One might be taken for English" .)