Exam with Open University leaving you grumpy (5)
I believe the answer is:
testy
'grumpy' is the definition.
(testy can mean irritable or annoyed)
'exam with open university leaving you' is the wordplay.
'exam' becomes 'test' (synonyms).
'with' says to put letters next to each other.
'open university' becomes 'OU'.
'leaving' indicates named letters should be taken away.
'you' with 'ou' taken out is 'y'.
'test'+'y'='TESTY'
(Other definitions for testy that I've seen before include "Showing irritation" , "Irritably impatient" , "Easily irritated" , "Captious" , "Short-tempered" .)