The most common and most likely answer to this crossword clue is the 4 plus 2 letter word USED TO
I've seen this crossword clue in The Daily Telegraph
U
S
E
D
T
O
More clues leading to the result USED TO
- Familiar with being roughly ousted
- Familiar with American chaps ignoring Miles
- U Accustomed, being ousted out
- Taken over by American news boss, holy publication did
- Would take essence of arrowroot desultorily in retirement
- Acquainted with duo set in motion
- Comfortable with ‘Our Party’, Miliband’s almost premier
- In the habit of playing duets with nothing on
- Settle dues, to get accustomed
- At home with American edition books to go over
Buddy explains!

The straight part
We know that "Familiar with" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case familiar with = used to.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.