The most common and most likely answer to this crossword clue is the 6 letter word GROINS
I've seen this crossword clue in Financial Times
G
R
O
I
N
S
Buddy explains!
The straight part
We know that "Privates" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case privates = groins.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 GROINS mean?
GROINS noun- The crease or depression of the human body at the junction of the trunk and the thigh, together with the surrounding region.
- The area adjoining this fold or depression.
- The projecting solid angle formed by the meeting of two vaults
- The genitals.
- The surface formed by two such vaults.
- An often wooden structure that projects from a coastline to prevent erosion, longshore drift etc.; a breakwater.