Big cat in the past seen around university (5)
I believe the answer is:
ounce
'big cat' is the definition.
(ounce is a kind of big cat)
'past seen around university' is the wordplay.
'past' becomes 'once' ('once' can be similar in meaning to 'past').
'seen around' indicates putting letters inside.
'university' becomes 'u'.
'once' enclosing 'u' is 'OUNCE'.
'in the' is the link.
(Other definitions for ounce that I've seen before include "Wild cat - small weight" , "16 for a pound" , "little weight" , "A light weight - feline" , "one of a number in the pound" .)