Last to finish by river (6)
I believe the answer is:
endure
'last' is the definition.
(enduring is a kind of lasting)
'finish by river' is the wordplay.
'finish' becomes 'end' (come to an end).
'by' means one lot of letters go next to another.
'river' becomes 'ure' (river in Yorkshire).
'end'+'ure'='ENDURE'
'to' is the link.
(Other definitions for endure that I've seen before include "Put up with something" , "Suffer, tolerate" , "Last or suffer patiently" , "Go through" , "Tolerate, put up with" .)