The most common and most likely answer to this crossword clue is the 8 letter word EXACTION
I've seen this crossword clue in Financial Times
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More clues leading to the result EXACTION
- Rigorous one performing oppressive demand
- Demand made by ditched lover maybe leading to lawsuit
- Former partner having case for enforcement of payment
- Former partner with case making excessive demand
- Vote in English lawsuit for enforcement of payment
- I once laboured with tax demand that’s excessive
- Demand lawsuit against former lover
- Old case of extortion
- Blackmail could be former lover's doing
- Demand made in divorce court case?
Buddy explains!

The straight part
We know that "oppressive demand" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case oppressive demand = exaction.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 EXACTION mean?
EXACTION noun- The act of demanding with authority, and compelling to pay or yield; compulsion to give or furnish; a levying by force
- Extortion.
- That which is exacted; a severe tribute; a fee, reward, or contribution, demanded or levied with severity or injustice.