Swimmer takes jog around university (5)
I believe the answer is:
trout
'swimmer' is the definition.
(trout is a kind of aquatic vertebrate)
'jog around university' is the wordplay.
'jog' becomes 'trot' ('trot' can be a synonym of 'jog').
'around' means one lot of letters goes inside another.
'university' becomes 'u'.
'trot' enclosing 'u' is 'TROUT'.
'takes' is the link.
(Other definitions for trout that I've seen before include "Tickled fish?" , "Rainbow, say" , "Small salmonlike fish" , "Tasty fish, brown or rainbow" , "Game fish related to salmon" .)