Bury requirement not to finish off prisoner (8)
I believe the answer is:
internee
'prisoner' is the definition.
(internee is a kind of prisoner)
'bury requirement not to finish off' is the wordplay.
'bury' becomes 'inter' (synonyms).
'requirement' becomes 'need' (synonyms).
'not to finish off' means to remove the last letter (the word doesn't finish).
'need' with its final letter removed is 'nee'.
'inter'+'nee'='INTERNEE'
(Other definitions for internee that I've seen before include "Imprisoned person" , "One imprisoned during wartime" , "Detainee" , "Prisoner of war living in armed camp or prison" , "Alien confined in war" .)