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9a Run around academy and trace compound (10)
I have: ?O?F?A???A
4a Ornament with cross given to a torturer (10)
I have: T???U?M???
21a Winner's characteristic in opposition (4-2-4)
I have ?A?E-?O-?A?E I can only think of FACE-TO FACE but can't parse it

4 torquemada?

Are you sure of the final A in 9? Most compounds end in ITE or ATE - e.g. wolframite?)

flow backwards, Royal Academy, MITE

torque (ornament, though I would spell that TORC), MAD - cross, A

Many thanks.
21a Winner's characteristic in opposition (4-2-4)
I have ?A?E-?O-?A?E I can only think of FACE-TO FACE but can't parse it

Well, face-to-face is "in opposition", but I don't see the rest.

break it down this way

Facet of Ace
Characteristic of a winner

Clever mamya!

facet of (an) ace