Wherein to fight a hard-hearted woman (5)

I believe the answer is:

arena

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'wherein to fight a' is the definition.
I can't tell whether this defines the answer.

'hard-hearted woman' is the wordplay.
'hearted' means to look at the middle letters.
'woman' becomes 'ena' (feminine given name).
The centre of 'hard' is 'ar'.
'ar'+'ena'='ARENA'

Can you help me to learn more?

(Other definitions for arena that I've seen before include "Performance space" , "Sit around here being entertained" , "Sporting enclosure" , "Place of combat" , "An era (anag.)" .)

I've seen this clue in the Evening Standard.

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