The most common and most likely answer to this crossword clue is the 2 plus 3 plus 6 plus 4 letter word TO THE MANNER BORN
I've seen this crossword clue in The Guardian
T
O
T
H
E
M
A
N
N
E
R
B
O
R
N
Buddy explains!
The straight part
We know that "Familiar from birth wi/t/h/line from Hamlet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case familiar from birth wi/t/h/line from hamlet = to the manner born.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.