Delegate stuck in river (6)
I believe the answer is:
depute
'delegate' is the definition.
(synonyms)
'stuck in river' is the wordplay.
'stuck' becomes 'put' ('stick' and 'put' can both mean to place).
'in' is an insertion indicator.
'river' becomes 'dee' (River Dee).
'put' placed into 'dee' is 'DEPUTE'.
(Other definitions for depute that I've seen before include "Delegate task to someone" , "Delegate to, appoint as representative" , "Appoint to act on one's behalf" .)