US, for example, wanting inn as reminder of the past (5)

I believe the answer is:

relic

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'reminder of the past' is the definition.
'relic' can be an answer for 'reminder' (thesaurus). I'm unsure of the 'of the past' bit.

I can't explain the remainder of the clue.

Can you help me to learn more?

(Other definitions for relic that I've seen before include "Personal saintly memorial" , "Survival from an earlier time" , "Memorial of antiquity" , "Memento; souvenir" , "A survival from the past" .)

I've seen this clue in The Times.

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