Extremely succinct impression about university trainee (7)
I believe the answer is:
student
'trainee' is the definition.
(a student is in training)
'extremely succinct impression about university' is the wordplay.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'impression' becomes 'dent' (dent is a kind of impression).
'about' means one lot of letters go next to another.
'university' becomes 'U' (abbreviation as in UMass).
'succinct' with its middle taken out is 'st'.
'dent' put after 'u' is 'udent'.
'st'+'udent'='STUDENT'
(Other definitions for student that I've seen before include "Person engaged in learning" , "Learner, pupil" , "One at university" , "Trainee" , "Scholar" .)