Overstay? It's quite the opposite experience (7)

I believe the answer is:

undergo

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'experience' is the definition.
(to undergo something is to experience it)

I don't understand the rest of the clue.

(Other definitions for undergo that I've seen before include "Withstand" , "Submit to an experience" , "put up with" , "Experience or live through" , "Guerdon (anag.)" .)

I've seen this clue in The Irish Times.

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