Problem after river's lowest (7)
I believe the answer is:
deepest
'lowest' is the definition.
('deep' can be similar in meaning to 'low')
'problem after river's' is the wordplay.
'problem' becomes 'pest' (both can mean an annoyance).
'after' says to put letters next to each other.
'river' becomes 'dee' (River Dee).
'pest' put after 'dee' is 'DEEPEST'.
(Other definitions for deepest that I've seen before include "most hard to fathom" , "Most learned" , "Most profound" , "hardest to understand" , "Most intense" .)