The most common and most likely answer to this crossword clue is the 11 letter word GRANDMOTHER
I've seen this crossword clue in The Times
G
R
A
N
D
M
O
T
H
E
R
More clues leading to the result GRANDMOTHER
Buddy explains!

The straight part
We know that "Matriarch possibly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case matriarch possibly = grandmother.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 GRANDMOTHER mean?
GRANDMOTHER noun- A mother of someone's parent.
- A female ancestor or progenitor.