21a Get the better of (3,4) W?N ?P?N
The only answer I can think of is WIN OPEN. While I know it's getting the better of an opponent it seems the wrong answer!!
28a. Resident of Athens, Sparta or Lebanon, say (10) ?E?N?S?E?N
I have put TENNESSEAN for the only reason that "say" is in the clue but it is the other side of the world to the clue.
The "P" is correct I think as 22d. English actress who played Desdemona opposite Paul Robeson's Othello in 1931 (5,8) Answer is Peggy Ashcroft. But I do think your answer is good.