Endure, long after date that's absolutely final (4-5)
I believe the answer is:
last-ditch
'that's absolutely final' is the definition.
(as in a last-ditch attempt)
'endure long after date' is the wordplay.
'endure' becomes 'last' (synonyms).
'long' becomes 'itch' (to long or itch for something is to desire it).
'after' means one lot of letters go next to another.
'date' becomes 'd' (abbreviation e.g. dob - date of birth).
'itch' after 'd' is 'ditch'.
'last'+'ditch'='LAST-DITCH'
(Other definitions for last-ditch that I've seen before include "Eleventh-hour" , "Denoting final attempt (to do something)" , "Of an attempt or stand, final and desperate" , "Final recourse" , "Eleventh hour" .)