Hesitate at murder, not finishing off (5)
I believe the answer is:
demur
'hesitate' is the definition.
(thesaurus)
'murder not finishing off' is the wordplay.
'not finishing' means to remove the last letter.
'off' indicates an anagram.
'murder' with its last letter taken off is 'murde'.
'murde' anagrammed gives 'DEMUR'.
'at' is the link.
(Other definitions for demur that I've seen before include "Raise scruples" , "Hesitate from uncertainty or object" , "Cavil, dispute" , "Balk" , "Politely disagree" .)