Not a public soldier! (7)

I believe the answer is:

private

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'soldier' is the definition.
(I've seen this before)

I cannot understand how the rest of the clue works.

(Other definitions for private that I've seen before include "Clandestine" , "Secret - soldier of the lowest rank" , "To most, unknown" , "Army three Dn" , "Rank, concealed" .)

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

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