The most common and most likely answer to this crossword clue is the 10 letter word PEREMPTORY
I've seen this crossword clue in The Daily Telegraph
P
E
R
E
M
P
T
O
R
Y
More clues leading to the result PEREMPTORY
- Bossy old man abroad, politician, one on the right wing
- Autocratic politician — conservative — follows dad overthe Channel
- Assertive father to French politician, right-winger
- Final free property to house them
- Guardiola hedging about debut of Moroccan right-winger in final
- High-handed European politician, Conservative, chasing a lot of perks?
- A group of soldiers occupying hollow, brooking no opposition
- Nancy's father finds politicianimperious
- Haughty peer blasted member of Parliament and Boris Johnson, e.g.
Buddy explains!

The straight part
We know that "High-handed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case high-handed = peremptory.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 PEREMPTORY mean?
PEREMPTORY noun- A challenge to the admission of a juror, without the challenger needing to show good cause.
- Precluding debate or expostulation; not admitting of question or appeal
- Positive in opinion or judgment; absolutely certain, overconfident, unwilling to hear any debate or argument (especially in a pejorative sense); dogmatic.
- Firmly determined, resolute; obstinate, stubborn.
- Accepting no refusal or disagreement; imperious, dictatorial.