Egg cage is not shut (4)
I believe the answer is:
open
'is not shut' is the definition.
('open' is the opposite to 'shut')
'egg cage' is the wordplay.
'egg' becomes 'o' (an 'o' resembles an egg).
'cage' becomes 'pen' (I've seen this before).
'o'+'pen'='OPEN'
(Other definitions for open that I've seen before include "yawning" , "Honest - frank" , "Frank; not closed" , "Freely accessible" , "Not secret or hidden" .)