One objects to secret set or private group’s promotion (9)

I believe the answer is:

protester

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'group's promotion' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

'one objects to secret set or private' is the wordplay.
'PROTESTER' is hidden back-to-front within the letters.
But, I'm not sure how this is indicated.

Can you help me to learn more?

(Other definitions for protester that I've seen before include "I strongly object" , "Demonstrating kind" , "Demonstrator" , "Dissident" , "objector" .)

I've seen this clue in the Sydney Morning Herald.

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