The most common and most likely answer to this crossword clue is the 11 letter word IMPERIALIST
I've seen this crossword clue in Financial Times
I
M
P
E
R
I
A
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T
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The straight part
We know that "despot" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case despot = imperialist.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 IMPERIALIST mean?
IMPERIALIST noun- An advocate of imperialism.
- Of, or relating to imperialism.