American university’s party ending with drink (4)
I believe the answer is:
yale
'american university's' is the definition.
(I've seen this before)
'party ending with drink' is the wordplay.
'ending' indicates one should take the final letters.
'with' means one lot of letters go next to another.
'drink' becomes 'ale' (ale is a kind of drink).
The final letter of 'party' is 'y'.
'y'+'ale'='YALE'
(Other definitions for yale that I've seen before include "Thief might gain entrance after picking this" , "New Haven university" , "University man" , "US university; lock" , "Member of the 11 - type of lock" .)