Appearance of a Republican opponent (7)
I believe the answer is:
arrival
'appearance' is the definition.
(to appear can mean to arrive at a particular place)
'a republican opponent' is the wordplay.
'republican' becomes 'R' (abbreviation).
'opponent' becomes 'rival' (a rival is an opponent or enemy).
'a'+'r'+'rival'='ARRIVAL'
'of' acts as a link.
(Other definitions for arrival that I've seen before include "Act of coming" , "The reaching of one's destination" , "Achievement of destination" , "Advent" , "Appearance (at a destination)" .)