The most common and most likely answer to this crossword clue is the 12 letter word ACQUAINTANCE
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result ACQUAINTANCE
Buddy explains!
The straight part
We know that "Familiarity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case familiarity = acquaintance.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 ACQUAINTANCE mean?
ACQUAINTANCE noun- A state of being acquainted with a person; originally indicating friendship, intimacy, but now suggesting a slight knowledge less deep than that of friendship; acquaintanceship.
- A person or persons with whom one is acquainted.
- Such people collectively; one's circle of acquaintances (with plural concord).
- Personal knowledge (with a specific subject etc.).