The most common and most likely answer to this crossword clue is the 9 letter word PRIVATISE
I've seen this crossword clue in The Guardian
P
R
I
V
A
T
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Buddy explains!

The straight part
We know that "Dispossess the people of" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dispossess the people of = privatise.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 PRIVATISE mean?
PRIVATISE verb- To release government control of (a business or industry) to private industry.
- To make (a variable, etc.) private in scope.