May be shut, therefore (4)
I believe the answer is:
thus
'therefore' is the definition.
('thus' can be a synonym of 'therefore')
'may be shut' is the wordplay.
'may' is an anagram indicator (I've seen 'might' mean this (I've seen this in other clues)).
'shut' anagrammed gives 'THUS'.
(Other definitions for thus that I've seen before include "Therefore, hence" , "as indicated" , "It follows" , "'So, therefore (4)'" , "As a result" .)