The most common and most likely answer to this crossword clue is the 7 letter word LOCK-IN
I've seen this crossword clue in The Times
L
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More clues leading to the result LOCK-IN
Buddy explains!

The straight part
We know that "time for private drink" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case time for private drink = lock-in.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 LOCK-IN mean?
LOCK-IN noun- A sleepover party, usually held in a public place such as a church or school, in which the participants are not allowed to leave until the next morning.
- An illegal but widely-tolerated invitation-only gathering in a British pub, after the end of licensing hours, to allow regular customers the opportunity to enjoy further drinking time.
- A situation in which members of an industry have agreed to adopt a certain standard and have retooled their production to meet this standard, thus making it very costly to change to a different standard.