Endures, though finishing at one's wits' end (5)
I believe the answer is:
lasts
'endures' is the definition.
('last' can be a synonym of 'endure')
'at one's wits' end' is the wordplay.
'at' says to put letters next to each other.
'one's wits'' becomes 's' (I can't justify this - if you can you should believe this answer much more).
'end' becomes 'last' (I've seen this before).
's' put after 'last' is 'LASTS'.
'though finishing' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for lasts that I've seen before include "Keeps on" , "Endures" , "Goes on" , "Holds out" , "carries on" .)