10 across
Top
female
Republican
with
manic
air
enters
contest
(9)
Top female Republican with manic air enters contest (9)
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The definition is at the beginning of the clue.
How the clue works
Top female is your definition — think dominant head of a family. You've got R for Republican, then a manic anagram of air giving RIAR, and the whole lot "enters" contest (MATCH) to give you MAT(RIAR)CH.