Skint, no first kid - it's an injury (6,3)

I believe the answer is:

broken rib

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'an injury' is the definition.
I don't know anything about this answer so I can't judge whether it can be defined by this definition.

'skint no first kid' is the wordplay.
'skint' becomes 'broke' (synonyms).
'no first' becomes 'n' (1st letter of 'no').
'kid' becomes 'rib' (both can mean to tease or mock).
'broke'+'n'+'rib'='BROKEN RIB'

'it's' acts as a link.

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

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