Miss America is alluring, Republican's admitted (3,4)
I believe the answer is:
air shot
'miss' is the definition.
(an instance of missing a ball in sport)
'america is alluring republican's admitted' is the wordplay.
'america' becomes 'a' (common abbreviation - e.g. in organisation names).
'alluring' becomes 'hot' (both can mean attractive).
'republican' becomes 'r' (abbreviation).
'admitted' is an insertion indicator.
'is'+'hot'='ishot'
'ishot' going around 'r' is 'irshot'.
'a'+'irshot'='AIR SHOT'
(Another definition for air shot that I've seen is " Golf stroke that misses the ball".)