Most profound river problem (7)
I believe the answer is:
deepest
'most profound' is the definition.
('deep' can be a synonym of 'profound')
'river problem' is the wordplay.
'river' becomes 'dee' (River Dee).
'problem' becomes 'pest' (both can mean an annoyance).
'dee'+'pest'='DEEPEST'
(Other definitions for deepest that I've seen before include "at the very bottom" , "most insidious" , "most demanding" , "hard to get, in the extreme" , "Most learned" .)