One promising not to start book (6)
I believe the answer is:
ledger
'book' is the definition.
(synonyms)
'one promising not to start' is the wordplay.
'one promising' becomes 'pledger' (I've seen this before).
'not to start' means to remove the first letter.
'pledger' with its first letter taken away is 'LEDGER'.
(Other definitions for ledger that I've seen before include "Business record book" , "Account book" , "Accounting journal" , "Old-fashioned heavy accounts book" , "Book for keeping financial accounts" .)