Bear is close to river (6)
I believe the answer is:
endure
'bear' is the definition.
('endure' can be a synonym of 'bear')
'close to river' is the wordplay.
'close' becomes 'end' (I've seen this before).
'to river' becomes 'ure' (I have seen 'River of Wensleydale ' mean 'ure' so perhaps 'river' could also mean 'ure').
'end'+'ure'='ENDURE'
'is' is the link.
(Other definitions for endure that I've seen before include "Undergo hardship patiently" , "Last or undergo" , "Go through" , "survive" , "Bear something patiently" .)