One allows donkey to get put down (8)
I believe the answer is:
assenter
'one allows' is the definition.
(someone who assents or agrees to something)
'donkey to get put down' is the wordplay.
'donkey' becomes 'ass' (ass is a term for a donkey).
'to get' is a charade indicator (letters next to each other).
'put down' becomes 'enter' (synonyms).
'ass'+'enter'='ASSENTER'
(Other definitions for assenter that I've seen before include "he's quite agreeable" , "One who agrees" .)