Bard's river (4)
I believe the answer is:
'bard's river' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for avon that I've seen before include "Shakespeare its swan" , "[WILTS] flower" , "River flowing through Bristol to the Severn" , "Name of several English rivers" , "Bristol's river" .)