The most common and most likely answer to this crossword clue is the 10 letter word MATRIFOCAL
I've seen this crossword clue in The Times
M
A
T
R
I
F
O
C
A
L
Buddy explains!
The straight part
We know that "centred on the mum" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case centred on the mum = matrifocal.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 MATRIFOCAL mean?
MATRIFOCAL adjective- Matriarchal