Fear losing head for study (4)
I believe the answer is:
read
'study' is the definition.
('read' can be a synonym of 'study')
'fear losing head' is the wordplay.
'fear' becomes 'dread' ('dread' can be a synonym of 'fear').
'losing head' means to remove the first letter.
'dread' with its first letter removed is 'READ'.
'for' is the link.
(Other definitions for read that I've seen before include "Examine" , "See - peruse - understand" , "Study (for a degree?)" , "examined" , "(Of passage) have a certain wording" .)