Entrust study to Castro mostly (7)
I believe the answer is:
confide
'entrust' is the definition.
('confide' can be a synonym of 'entrust')
'study to castro mostly' is the wordplay.
'study' becomes 'con' (I've seen this before).
'to castro' becomes 'fidel' (Fidel Castro famous ruler of Cuba).
'mostly' means to remove the last letter.
'fidel' with its last letter taken away is 'fide'.
'con'+'fide'='CONFIDE'
(Other definitions for confide that I've seen before include "Trust wholly (in person)" , "Tell secret or entrust to" , "Tell secret as to friend - mum's the word" , "Impart secrets to someone" .)