So as to show some enthusiasm (4)
I believe the answer is:
thus
'so' is the definition.
(synonyms)
'to show some enthusiasm' is the wordplay.
'to show some' indicates a hidden word (I've seen this in other clues).
'THUS' can be found hidden inside 'enthusiasm'.
'as' acts as a link.
(Other definitions for thus that I've seen before include "Consequently" , "As a result" , "Therefore, hence" , "as indicated" , "Shut (anag.)" .)