Constant companion of Irish playwright holding party (6)
I believe the answer is:
shadow
'constant companion' is the definition.
'irish playwright holding party' is the wordplay.
'irish playwright' becomes 'shaw' (George Bernard Shaw).
'holding' indicates putting letters inside.
'party' becomes 'do' (do is a kind of party).
'shaw' going around 'do' is 'SHADOW'.
'of' acts as a link.
(Other definitions for shadow that I've seen before include "Reflected image" , "Sort of boxer - dog" , "Dark shape (on the Opposition front bench?)" , "Darker part" , "Image caused by obscuring of light" .)