Having turned up, shoved into an outhouse! (4)

I believe the answer is:

shed

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'outhouse' is the definition.
(thesaurus)

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

(Other definitions for shed that I've seen before include "In which tools may be" , "Kind of hut - discard it" , "Jettison" , "Discard (something)" , "Discarded" .)

I've seen this clue in the Evening Standard.

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