The most common and most likely answer to this crossword clue is the 9 letter word DESPOTISM
I've seen this crossword clue in The Guardian
D
E
S
P
O
T
I
S
M
More clues leading to the result DESPOTISM
Buddy explains!

The straight part
We know that "Power" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case power = despotism.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 DESPOTISM mean?
DESPOTISM noun- Government by a singular authority, either a single person or tight-knit group, which rules with absolute power, especially in a cruel and oppressive way.