Each hasn’t begun so (4)
I believe the answer is:
very
'so' is the definition.
(I've seen this before)
'each hasn't begun' is the wordplay.
'each' becomes 'every' (synonyms).
'hasn't begun' means to remove the first letter.
'every' with its first letter taken away is 'VERY'.
(Other definitions for very that I've seen before include "Sort of light" , "Exceedingly" , "Real" , "Ever so" , "Frightfully" .)