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With raincoat on, Elizabeth heads off to a play (7)


I believe the answer is:


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'a play' is the definition.
(Shakespeare play)

'with raincoat on elizabeth heads off' is the wordplay.
I cannot quite understand how this works, but
'raincoat' could be 'mac' (macintosh is a type of raincoat) and 'mac' is found in the answer.
'elizabeth' could be 'bet' (I've seen this in other clues) and 'bet' is located in the answer.
A single letter 'h' remains which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

'to' is the link.

Can you help me to learn more?

(Other definitions for macbeth that I've seen before include "Shakespears's Scottish play" , "Shakespearean tragedy" , "Shakespeare play" , "Shakespeare's Scottish play, considered unlucky" , "King of Scotland, 1040-1057" .)

I've seen this clue in the Sydney Morning Herald.
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