Possible Clues:

• 1980s Treasury head Donald
• Keep complaining queen's upset king's daughter
• Anger created by cruel daughter
• Goneril's sister
• The Duke of Cornwall's wife, in Shakespeare
• Cordelia's sister, almost majestic by name
• Manageress has taken up role at Stratford
• Reagan's first Treasury secretary
• Shakespearean baddie to win once more? Not I
• Wife of the Duke of Cornwall, in Shakespeare