Study Yankee’s to declare false (4)
I believe the answer is:
deny
'to declare false' is the definition.
'study yankee's' is the wordplay.
'study' becomes 'den' (I've seen this before**).
'yankee' becomes 'y' (phonetic alphabet: alpha, bravo, charlie etc.).
'den'+'y'='DENY'
(Other definitions for deny that I've seen before include "Gainsay" , "Declare untrue" , "Refute, contradict" , "Refuse to admit the truth" , "Refuse to grant" .)