Reluctant to drop opening promise (4)
I believe the answer is:
oath
'promise' is the definition.
(I know that oath is a type of promise)
'reluctant to drop opening' is the wordplay.
'reluctant' becomes 'loath' (synonyms).
'to drop opening' means to remove the first letter.
'loath' with its first letter taken away is 'OATH'.
(Other definitions for oath that I've seen before include "A curse or a vow" , "It's taken in court" , "in court, we take it" , "Commitment to tell the truth" , "Imprecation" .)