Sieve fits badly (4)
I believe the answer is:
sift
'sieve' is the definition.
('sift' can be a synonym of 'sieve')
'fits badly' is the wordplay.
'badly' indicates anagramming the letters.
'fits' anagrammed gives 'SIFT'.
(Other definitions for sift that I've seen before include "Analyse carefully in fist" , "Separate by passing through fine mesh" , "Use fist to pass through perforated container" , "Sieve finely" , "Pass though a sieve" .)