A new promise to leave a reply (6)
I believe the answer is:
answer
'reply' is the definition.
(answer is a kind of reply)
'a new promise to leave a' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'promise' becomes 'swear' (as in swearing something is true).
'to leave' indicates named letters should be taken away (some letters are left out).
'swear' with 'a' taken out is 'swer'.
'a'+'n'+'swer'='ANSWER'
(Other definitions for answer that I've seen before include "'A soft . . . . . . turneth away wrath'" , "Respond" , "Response to a question" , "It could give you a" , "Reply or solution" .)