Arrives carrying actor’s part showing fair quality (10)
I believe the answer is:
comeliness
'fair quality' is the definition.
(quality of being fair or comely)
'arrives carrying actor's part' is the wordplay.
'arrives' becomes 'comes' ('come' can be a synonym of 'arrive').
'carrying' indicates putting letters inside.
'actor's part' becomes 'lines' (lines learned by an actor).
'comes' enclosing 'lines' is 'COMELINESS'.
'showing' is the link.
(Other definitions for comeliness that I've seen before include "good looks?" , "Beauty" .)