Town to have second university in time (8)
I believe the answer is:
monmouth
'town' is the definition.
(I've seen this before)
'second university in time' is the wordplay.
'second' becomes 'mo' (both are short periods of time).
'university' becomes 'u' (abbreviation for university).
'in' is an insertion indicator.
'time' becomes 'month' (I can't justify this - if you can you should give a lot more credence to this answer).
'mo'+'u'='mou'
'mou' put inside 'month' is 'MONMOUTH'.
'to have' is the link.
Can you help me to learn more?
(Other definitions for monmouth that I've seen before include "Welsh town; a rebellious Duke" , "Town in Wales" .)