State with new shed for dairy cow (6)

I believe the answer is:

jersey

'for dairy cow' is the definition.
(Jersey is an example)

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

(Other definitions for jersey that I've seen before include "Garment for upper body" , "farm animal" , "Jumper or top" , "lower?" , "Channel Island - jumper" .)

I've seen this clue in The Guardian.

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