OK friends, thanks for your answers so far. A couple more.
1D - Miss Pargeter entered his field (6) I have P?T?E? Is there a confusion here with Simon Brett's MRS. Pargeter novels ?
7D - Mother of Cleopatra and Alexander to be seen in London arena on Saturday (8) I have ??Y?P?A?
16D - second highest American friend as dramatist (8) I have ?T?P????
17D - is he in Leinster ? not entirely, thuis Friday writer (8) I have ?E?N????
Not doing very well so far, am I !