Rode around the river (4)
I believe the answer is:
oder
'the river' is the definition.
(Oder is an example)
'rode around' is the wordplay.
'around' indicates anagramming the letters.
'rode' with letters rearranged gives 'ODER'.
(Other definitions for oder that I've seen before include "German banker" , "river, one in central Europe" , "waterway" , "River on border of Poland and Germany" , "School blazer insignia" .)