Maintain study to mind (7)
I believe the answer is:
contend
'maintain' is the definition.
(I've seen this before)
'study to mind' is the wordplay.
'study' becomes 'con' (con can informally mean to study).
'to mind' becomes 'tend' (to tend is to look after or mind somebody).
'con'+'tend'='CONTEND'
(Other definitions for contend that I've seen before include "Compete, vie" , "Struggle in rivalry" , "Tend NCO (anag.)" , "Compete; deal (with)" , "fight" .)