Refuse to acknowledge study's ending in ignominy (4)
I believe the answer is:
deny
'refuse to acknowledge' is the definition.
(I've seen this in another clue)
'study's ending in ignominy' is the wordplay.
'study' becomes 'den' (term for a study or office).
'ending in' suggests the final letters.
The final letter of 'ignominy' is 'y'.
'den'+'y'='DENY'
(Other definitions for deny that I've seen before include "Refuse to accept" , "Reject as true" , "Refuse to admit (something)" , "Disclaim" , "Controvert" .)