Cold run? I'll put on overcoat! (7)

I believe the answer is:

cladder

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'i'll put on overcoat' is the definition.
I can't judge whether this definition defines the answer.

'cold run?' is the wordplay.
'cold' becomes 'C' (eg on taps).
'run?' becomes 'ladder' (both can mean a rip in tights).
'c'+'ladder'='CLADDER'

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I've seen this clue in The Independent.

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