The most common and most likely answer to this crossword clue is the 8 letter word INTIMACY
I've seen this crossword clue in The Times
I
N
T
I
M
A
C
Y
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 = intimacy.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 INTIMACY mean?
INTIMACY noun- Feeling or atmosphere of closeness and openness towards someone else, not necessarily involving sexuality.
- Intimate relationship.
- (especially plural) Intimate detail, (item of) intimate information.