Totally rush round university with student (5)
I believe the answer is:
fully
'totally' is the definition.
(thesaurus)
'rush round university with student' is the wordplay.
'rush' becomes 'fly' (both can mean to hurry).
'round' is an insertion indicator.
'university' becomes 'U' (abbreviation for university).
'with' says to put letters next to each other.
'student' becomes 'L' (as in L-plates for learner drivers).
'u'+'l'='ul'
'fly' going around 'ul' is 'FULLY'.
(Other definitions for fully that I've seen before include "Wholly" , "Completely" , "Entirely" , "In all respects" .)