Nearly caught in open, suddenly (9)
I believe the answer is:
overnight
'suddenly' is the definition.
('overnight' can be a synonym of 'suddenly')
'nearly caught in open' is the wordplay.
'nearly' becomes 'nigh' ('nigh' can be a synonym of 'nearly').
'caught in' indicates putting letters inside.
'open' becomes 'overt' ('overt' is associated in meaning with 'open').
'nigh' put within 'overt' is 'OVERNIGHT'.
(Other definitions for overnight that I've seen before include "Lightning" , "Until morning; suddenly" , "Very quickly" , "darkness" , "until tomorrow" .)