To be honest, there's nothing to write (4)
I believe the answer is:
open
'to be honest' is the definition.
('open' can be similar in meaning to 'honest')
'nothing to write' is the wordplay.
'nothing' becomes 'o' (looks like zero - 0).
'to' says to put letters next to each other.
'write' becomes 'pen' ('pen' can be a synonym of 'write').
'o'+'pen'='OPEN'
'there's' is the link.
(Other definitions for open that I've seen before include "Freely accessible" , "hardly high-security" , "'Frank, not secret (4)'" , "Plain" , "Not closed or secret" .)