Appearance of a Republican challenger (7)
I believe the answer is:
arrival
'appearance' is the definition.
(I've seen this before)
'a republican challenger' is the wordplay.
'republican' becomes 'r' (abbreviation).
'challenger' becomes 'rival' ('rival' can be a synonym of 'challenger').
'a'+'r'+'rival'='ARRIVAL'
'of' is the link.
(Other definitions for arrival that I've seen before include "Entry" , "Act of coming" , "The reaching of one's destination" , "Someone who's just come" , "The A in ETA" .)