Appearance of a Republican opponent (7)
I believe the answer is:
'appearance' is the definition.
(I've seen this before)
'a republican opponent' is the wordplay.
'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 "Achievement of destination", "Coming - comer", "Entry", "The reaching of one's destination", "Advent".)