Refuse to believe study by unknown (4)
I believe the answer is:
deny
'refuse to believe' is the definition.
(I've seen this in another clue)
'study by unknown' is the wordplay.
'study' becomes 'den' (term for a study or office).
'by' says to put letters next to each other.
'unknown' becomes 'y' (algebra).
'den'+'y'='DENY'
(Other definitions for deny that I've seen before include "Disown" , "Refuse to admit the truth" , "Forbid; not agree" , "Refuse to grant" , "Gainsay" .)