Run for an aid to climbing (6)

I believe the answer is:

ladder

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'run' is the definition.
(both can mean a rip in tights)

I don't understand how the rest of the clue works.

(Other definitions for ladder that I've seen before include "Domestic device for climbing" , "Household climbing device or hole in stocking" , "A run in a stocking" , "Opposite of snake?" , "Climbing structure" .)

I've seen this clue in The Times.

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