Loving doc treated chronic cough (4,5)

I believe the answer is:

long covid

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'chronic cough' is the definition.
I know nothing about this answer so I can't tell whether this works.

'loving doc treated' is the wordplay.
'treated' indicates an anagram.
'loving'+'doc'='lovingdoc'
'lovingdoc' is an anagram of 'LONG COVID'.

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

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