Least likely to persist (4)
I believe the answer is:
last
I believe this is a double definition.
'least likely' is the first definition.
(I've seen this in another clue)
'persist' is the second definition.
(I've seen this in another clue)
'to' is the link.
(Other definitions for last that I've seen before include "End" , "Endure - this clue is!" , "Shoemaker's shape" , "ending a series" , "Cargo to stay fresh" .)