The most common and most likely answer to this crossword clue is the 11 letter word TETE-A-TETE
T
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A
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More clues leading to the result TETE-A-TETE
- Rock not completely protecting tit or chat
- Repetitive notes written about adult in private meeting
- Repeatedly copied note about a private talk
- Four notes describing a meeting
- Four vacuous articles about adult conversation held in private
- Four notes about a private meeting
- Sofa for private conversation
- Notes taken about a restricted conversation?
- Three railway officials having drink, after removing their caps, in privacy
Buddy explains!

The straight part
We know that "private conversation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case private conversation = tete-a-tete.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 TETE-A-TETE mean?
TETE-A-TETE noun- A face-to-face meeting, or private conversation between two people, usually in an intimate setting; a head-to-head.
- A bench or sofa that allows two people to talk face-to-face.
- A variety of early flowering, fragrant daffodil.