Follow Kitty around university (6)
I believe the answer is:
pursue
'follow' is the definition.
(to pursue is to follow or chase)
'kitty around university' is the wordplay.
'kitty' becomes 'purse' (I can't justify this - if you can you should give a lot more credence to this answer).
'around' is an insertion indicator.
'university' becomes 'U' (abbreviation for university).
'purse' going around 'u' is 'PURSUE'.
Can you help me to learn more?
(Other definitions for pursue that I've seen before include "Follow up on or go after" , "Give chase" , "Follow, chase" , "Engage in or chase after" , "Search for" .)