Shut up, therefore (4)
I believe the answer is:
thus
'therefore' is the definition.
(synonyms)
'shut up' is the wordplay.
'up' indicates anagramming the letters (letters get chucked up).
'shut' with letters rearranged gives 'THUS'.
(Other definitions for thus that I've seen before include "As a result" , "'So, therefore (4)'" , "Consequently" , "In this way" , "as indicated" .)