The most common and most likely answer to this crossword clue is the 9 letter word JEWELLERS
I've seen this crossword clue in The Guardian
J
E
W
E
L
L
E
R
S
More clues leading to the result JEWELLERS
Buddy explains!

The straight part
We know that "Managers of the Stones" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case managers of the stones = jewellers.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 JEWELLERS mean?
JEWELLERS noun- A person whose job is making, repairing or selling jewelry.