Quietly belie running article that's working-class (8)

I believe the answer is:

plebeian

'working-class' is the definition.
(thesaurus)

'quietly belie running article' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'running' indicates an anagram.
'article' becomes 'an' (indefinite article).
'belie' is an anagram of 'lebei'.
'p'+'lebei'+'an'='PLEBEIAN'

'that's' is the link.

(Other definitions for plebeian that I've seen before include "Lower-class; commoner" , "Non-U?" , "Common person" , "not refined" , "Of the lower social classes, or uncultured" .)

I've seen this clue in The Telegraph.

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