The most common and most likely answer to this crossword clue is the 10 letter word CONVERSANT
I've seen this crossword clue in The Daily Telegraph
C
O
N
V
E
R
S
A
N
T
More clues leading to the result CONVERSANT
Buddy explains!

The straight part
We know that "Familiar" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case familiar = conversant.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.
Crossword Answer definitions
CONVERSANT noun- One who converses with another.
- Closely familiar; current; having frequent interaction
- Familiar or acquainted by use or study; well-informed; versed
- Concerned; occupied.