The river's a short way ahead (4)
I believe the answer is:
avon
'the river's' is the definition.
(I've seen this before)
'a short way ahead' is the wordplay.
'a short way' becomes 'av' (short for avenue; 'short' suggests an abbreviation).
'ahead' becomes 'on' (synonyms).
'av'+'on'='AVON'
(Other definitions for avon that I've seen before include "River of the Bard" , "English river name in multiple use" , "River joining Bath with Bristol" , "River flowing through Bristol to the Severn" , "Former English county" .)