The most common and most likely answer to this crossword clue is the 7 letter word TYRANNY
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Buddy explains!

The straight part
We know that "despotic regime" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case despotic regime = tyranny.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 TYRANNY mean?
TYRANNY noun- A government in which a single ruler (a tyrant) has absolute power; this system of government.
- The office or jurisdiction of an absolute ruler.
- Absolute power, or its use.
- A system of government in which power is exercised on behalf of the ruler or ruling class, without regard to the wishes of the governed.
- Extreme severity or rigour.