Shut as result of muggy day (6)
I believe the answer is:
closed
'shut' is the definition.
('closed' is associated in meaning with 'shut')
'muggy day' is the wordplay.
'muggy' becomes 'close'.
'day' becomes 'd'.
'close'+'d'='CLOSED'
'as result of' is the link.
(Other definitions for closed that I've seen before include "See 1" , "successfully completed" , "Terminated" , "restricted" , "Blocked off" .)