Was private flogged raw after exposing lies? (9)

I believe the answer is:

soldiered

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'was private' is the definition.
I can't judge whether this definition defines the answer.

'flogged raw after exposing lies?' is the wordplay.
'flogged' becomes 'sold' (flog can mean to sell).
'raw' becomes 'red' (I've seen this in another clue).
'after' means one lot of letters go next to another.
'exposing' says to take the centre (I've seen 'exposed' mean this (outside letters removed)).
The middle of 'lies' is 'ie'.
'red' after 'ie' is 'iered'.
'sold'+'iered'='SOLDIERED'

Can you help me to learn more?

I've seen this clue in The Independent.

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