Appearance of a Republican opponent (7)
I believe the answer is:
Here is my best explanation:
'appearance' is the definition.
'a republican opponent' is the subsidiary indication.
'republican' becomes 'r' (abbreviation).
'opponent' becomes 'rival' (I've seen this before).
'of' is the link.
(Other definitions for arrival that I've seen before include "Someone who's just come", "Attainment of destination", "The reaching of one's destination", "Advent", "The A in ETA", "Entry", "act", "achievement", "coming on the scene" and "entry".)