Hesitate, not beginning to change (5)
I believe the answer is:
alter
'change' is the definition.
(I know that change can be written as alter)
'hesitate not beginning' is the wordplay.
'hesitate' becomes 'falter' (faltering is a kind of hesitating).
'not beginning' means to remove the first letter.
'falter' with its first letter removed is 'ALTER'.
'to' acts as a link.
(Other definitions for alter that I've seen before include "Change, maybe later" , "Bout of extravagant spending" , "Make changes to" , "Amend" , "Revise" .)