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All answers having "Private ___" as clue:

3 Character Answers:

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EYE

OWN



4 Character Answers:

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EYES



5 Character Answers:

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INNER

LIVES



6 Character Answers:

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INSIDE

INWARD

SECRET

SECTOR



8 Character Answers:

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ONEONONE

PERSONAL

SQUADDIE



9 Character Answers:

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INNERMOST

NONPUBLIC



10 Character Answers:

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CLOSEDDOOR

ENTERPRISE

ONESTRIPER



12 Character Answers:

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ILLUSTRATION