So carelessly shut (4)
I believe the answer is:
thus
'so' is the definition.
('thus' can be a synonym of 'so')
'carelessly shut' is the wordplay.
'carelessly' is an anagram indicator.
'shut' with letters rearranged gives 'THUS'.
(Other definitions for thus that I've seen before include "'So, therefore (4)'" , "In this manner" , "Like so" , "Therefore, hence" , "It follows" .)