Last to finish by the river (6)
I believe the answer is:
endure
'last' is the definition.
(I know that last can be written as endure)
'finish by the river' is the wordplay.
'finish' becomes 'end' (synonyms).
'by' means one lot of letters go next to another.
'the river' becomes 'ure' (River Ure).
'end'+'ure'='ENDURE'
'to' acts as a link.
(Other definitions for endure that I've seen before include "Bear something patiently" , "Last or tolerate" , "Bear, suffer" , "Undergo hardship patiently" , "Put up with something" .)