Appearance of a Republican challenger (7)
I believe the answer is:
Here is my best explanation:
'appearance' is the definition.
'a republican challenger' is the subsidiary indication.
'republican' becomes 'r' (abbreviation).
'challenger' becomes 'rival' ('rival' can be a synonym of 'challenger').
'of' is the link.
(Other definitions for arrival that I've seen before include "Appearance, entrance", "Reaching a destination", "Act of coming", "Entrance", "The reaching of one's destination", "Advent", "entry", "Appearance (at a destination)", "The A in ETA" and "Someone who's just come".)