Frank has nothing to write with (4)
I believe the answer is:
open
'frank' is the definition.
('open' can be a synonym of 'frank')
'nothing to write with' is the wordplay.
'nothing' becomes 'o' (looks like zero - 0).
'to' says to put letters next to each other.
'write with' becomes 'pen' ('pen' can be a synonym of 'write'. I am not sure about the 'with' bit.).
'o'+'pen'='OPEN'
'has' is the link.
(Other definitions for open that I've seen before include "Golf tournament" , "with no clear favourite" , "Not shut or secret" , "Unfasten" , "Honest - frank" .)