The most common and most likely answer to this crossword clue is the 9 letter word GENEALOGY
I've seen this crossword clue in The Guardian
G
E
N
E
A
L
O
G
Y
Buddy explains!

The straight part
We know that "line" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case line = genealogy.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 GENEALOGY mean?
GENEALOGY noun- The descent of a person, family, or group from an ancestor or ancestors; lineage or pedigree.
- A record or table of such descent; a family tree.
- The study, and formal recording of such descents.