University awayday’s ending with beer! (4)
I believe the answer is:
yale
'university' is the definition.
(Yale is an example)
'awayday's ending with beer' is the wordplay.
'ending' suggests the final letters (the letter at the end of the word).
'with' is a charade indicator (letters next to each other).
'beer' becomes 'ale' (type of beer).
The last letter of 'awayday' is 'y'.
'y'+'ale'='YALE'
(Other definitions for yale that I've seen before include "Very important university" , "Mass. university" , "University man" , "US Ivy League university" , "Famous American university in Connecticut" .)