Keep going to the Nag’s Head and turning nasty (4)

I believe the answer is:

stay

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'keep going' is the definition.
(thesaurus)

I cannot understand how the remainder of the clue works.

(Other definitions for stay that I've seen before include "Linger" , "Abide" , "Remain; prop" , "Board; continue" , "Rope or wire used to support a mast" .)

I've seen this clue in the Evening Standard.

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