Students read this current old diary in Times (7)
I believe the answer is:
biology
'students read this' is the definition.
(subject which may be read at university)
'current old diary in times' is the wordplay.
'current old' becomes 'io' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'diary' becomes 'log' (I've seen this before).
'in' means one lot of letters goes inside another.
'times' becomes 'by' (both can mean 'multiplied by').
'io'+'log'='iolog'
'iolog' inserted within 'by' is 'BIOLOGY'.
(Other definitions for biology that I've seen before include "Study of living organisms" , "Science of living things" , "Study of living things" , "The science that studies living organisms" .)