Beat donkey after drink round river (7)
I believe the answer is:
surpass
'beat' is the definition.
(I know that surpass is a more specific form of beat)
'donkey after drink round river' is the wordplay.
'donkey' becomes 'ass' (ass is a term for a donkey).
'after' says to put letters next to each other.
'drink' becomes 'sup' (to sup is to drink).
'round' is an insertion indicator.
'river' becomes 'r' (abbreviation).
'sup' enclosing 'r' is 'surp'.
'ass' after 'surp' is 'SURPASS'.
(Other definitions for surpass that I've seen before include "Outstrip" , "Be better than (another)" , "Go one better" , "Transcend" , "supply best" .)