The most common and most likely answer to this crossword clue is the 4 letter word DENS
D
E
N
S
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The straight part
We know that "Private meeting-places" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case private meeting-places = dens.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 DENS mean?
DENS noun- A small cavern or hollow place in the side of a hill, or among rocks; especially, a cave used by a wild animal for shelter or concealment.
- A squalid or wretched place; a haunt.
- A comfortable room not used for formal entertaining.
- A narrow glen; a ravine; a dell.
- To ensconce or hide oneself in (or as in) a den.
- The strong odontoid process of the axis.