Frank Cook? Nope! (4)
I believe the answer is:
open
'frank' is the definition.
('open' can be a synonym of 'frank')
'cook? nope' is the wordplay.
'cook?' is an anagram indicator (I've seen 'cooked' mean this).
'nope' with letters rearranged gives 'OPEN'.
(Other definitions for open that I've seen before include "Freely accessible" , "Undo; exposed to attack" , "Start - frank" , "This championship includes both professional and amateur golfers" , "Not closed; set going" .)