Fearing degree being dropped at university (7)
I believe the answer is:
reading
'at university' is the definition.
(reading can mean studying a subject at university)
I cannot understand how the rest of the clue works.
(Other definitions for reading that I've seen before include "Interpreting text" , "university town" , "Recital" , "Studying for a degree - in Berkshire?" , "somewhere just off the M-four?" .)