Look after river sport (4)
I believe the answer is:
polo
'sport' is the definition.
(I know that polo is a type of equestrian sport)
'look after river' is the wordplay.
'look' becomes 'lo' (archaic exclamation meaning 'look!').
'after' means one lot of letters go next to another.
'river' becomes 'Po' (Italian river).
'lo' after 'po' is 'POLO'.
(Other definitions for polo that I've seen before include "explorer of the thirteenth century" , "Game, anagram of ..." , "It's played in water and on horseback" , "Game (with a hole?)" , "Game - Venetian traveller" .)