The most common and most likely answer to this crossword clue is the 10 letter word PATRIARCHY
I've seen this crossword clue in The Times
P
A
T
R
I
A
R
C
H
Y
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The straight part
We know that "man's rule" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case man's rule = patriarchy.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 PATRIARCHY mean?
PATRIARCHY noun- (history) A social system in which the father is head of the household, having authority over women and children, and in which lineage is traced through the male line.
- A power structure in which men are dominant.
- The office of a patriarch; a patriarchate.