A royal competitor's appearance (7)
I believe the answer is:
arrival
'appearance' is the definition.
(to appear can mean to arrive at a particular place)
'a royal competitor's' is the wordplay.
'royal' becomes 'r' (common abbreviation e.g. RM - Royal Marine).
'competitor' becomes 'rival' (synonyms).
'a'+'r'+'rival'='ARRIVAL'
(Other definitions for arrival that I've seen before include "coming on the scene" , "Coming - comer" , "Achievement of destination" , "The A in ETA" , "Advent" .)