Artist upset by competitor's appearance (7)
I believe the answer is:
arrival
'appearance' is the definition.
(I've seen this before)
'artist upset by competitor's' is the wordplay.
'artist' becomes 'ra' (Royal Academician, member of Royal Academy of Arts).
'upset' says the letters should be written in reverse.
'by' says to put letters next to each other.
'competitor' becomes 'rival' ('rival' can be a synonym of 'competitor'**).
'ra' written backwards gives 'ar'.
'ar'+'rival'='ARRIVAL'
(Other definitions for arrival that I've seen before include "Appearance, entrance" , "Coming - comer" , "Someone who's just come" , "Appearance (at a destination)" , "Appearance (at a place)" .)