In extremes of tragedy, she's sick at heart (5)

I believe the answer is:

tilly

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'in extremes of' is the definition.
The definition suggests a singular noun which matches the answer.

'tragedy she's sick at heart' is the wordplay.
'tragedy she' becomes 'ty' (I can't explain this - if you can you should believe this answer much more).
'sick' becomes 'ill' (synonyms).
'at heart' indicates putting letters inside (inserted letters go to the heart of the word).
'ty' enclosing 'ill' is 'TILLY'.

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I've seen this clue in the Evening Standard.

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