The most common and most likely answer to this crossword clue is the 6 letter word RANKER
I've seen this crossword clue in The Sunday Telegraph
R
A
N
K
E
R
Buddy explains!
The straight part
We know that "Private" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case private = ranker.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does RANKER mean?
RANKER adjective- Strong of its kind or in character; unmitigated; virulent; thorough; utter (used of negative things).
- Strong in growth; growing with vigour or rapidity, hence, coarse or gross.
- Suffering from overgrowth or hypertrophy; plethoric.
- Causing strong growth; producing luxuriantly; rich and fertile.
- Strong to the senses; offensive; noisome.
- Having a very strong and bad taste or odor.
- Complete, used as an intensifier (usually negative, referring to incompetence).
- Gross, disgusting.
- Strong; powerful; capable of acting or being used with great effect; energetic; vigorous; headstrong.
- Inflamed with venereal appetite; ruttish.
- One who ranks things, or arranges them in ranks
- A kind of soil developed over non-calcareous material, usually rock
- A common soldier
- One with a specified rank.