US university, without hesitation, showing excellence (5)
I believe the answer is:
merit
'excellence' is the definition.
(I've seen this in another clue)
'us university without hesitation' is the wordplay.
'us university' becomes 'MIT' (Massachusetts Institute of Technology).
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'hesitation' becomes 'er' (sound made while hesitating - um, er).
'mit' placed around 'er' is 'MERIT'.
'showing' acts as a link.
(Other definitions for merit that I've seen before include "Quality deserving reward" , "Rate" , "Deserve; excellence" , "Value" , "Have a right" .)