Lasts to finish out of place, sure! (7)
I believe the answer is:
endures
'lasts' is the definition.
('endure' can be a synonym of 'last')
'finish out of place sure' is the wordplay.
'finish' becomes 'end' (synonyms).
'out of place' indicates anagramming the letters.
'sure' is an anagram of 'ures'.
'end'+'ures'='ENDURES'
'to' is the link.
(Other definitions for endures that I've seen before include "Lasts or puts up with" , "Remains firm" , "Bears" , "Ensured (anag.)" , "Tolerates" .)