The most common and most likely answer to this crossword clue is the 7 plus 4 letter word MISSING LINK
I've seen this crossword clue in The Times
M
I
S
S
I
N
G
L
I
N
K
More clues leading to the result MISSING LINK
Buddy explains!

The straight part
We know that "Very old relative" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very old relative = missing link.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.