Stale conservative (6)

I believe the answer is:

stuffy

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This might be a double definition.

'stale' is the first definition.
(thesaurus)

'conservative' is the second definition.
Both the answer and definition are adjectives. Maybe there's a link between them I don't understand?

Can you help me to learn more?

(Other definitions for stuffy that I've seen before include "Airless - strait-laced" , "Lacking ventilation; narrow-minded" , "Airless - pompous" , "Badly ventilated" , "Airless - humourless" .)

I've seen this clue in The Irish Times.

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