Begin to write after the first of October (4)
I believe the answer is:
open
'begin' is the definition.
(both can mean to start)
'write after the first of october' is the wordplay.
'write' becomes 'pen' (synonyms).
'after' is a charade indicator (letters next to each other).
'the first of october' becomes 'o' (pst letter of 'october').
'pen' after 'o' is 'OPEN'.
'to' acts as a link.
(Other definitions for open that I've seen before include "Frank - unsettled" , "simple" , "Allowing access" , "Unfasten" , "William --, English poet" .)