Arrogant university needing external reminder (5)
I believe the answer is:
proud
'arrogant' is the definition.
(similar in meaning)
'university needing external reminder' is the wordplay.
I cannot really see how this works, but
'university' could be 'ou' and 'ou' is present in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for proud that I've seen before include "Feeling gratified or arrogant" , "Slightly projecting from a surface" , "Arrogant - sticking out" , "Haughty; projecting a little" , "Self-respect, feeling of self-worth" .)