High river battle (8)
I believe the answer is:
falsetto
'high' is the definition.
('falsetto' can be similar in meaning to 'high')
'river battle' is the wordplay.
'river' becomes 'fal' (I've seen this before).
'battle' becomes 'setto' (set-to is a kind of battle**).
'fal'+'setto'='FALSETTO'
(Other definitions for falsetto that I've seen before include "Artificial upper register of a male voice" , "Artificially high voice pitch" , "High vocal range" , "Unnatural voice" , "Way of singing at higher pitch" .)