The most common and most likely answer to this crossword clue is the 8 letter word INIQUITY
I've seen this crossword clue in The Times
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More clues leading to the result INIQUITY
- Entering island state, I abandon crime
- I left to support one probing city vice
- Holding my resignation announcement, I state it’s great injustice
- At home I’ve had enough: last seen of deadly sin
- Vice beginning to increase in New York — I’m going!
- Announce resignation in city, after one evil act
- I’m giving up, overwhelmed by current state of US injustice
- Sin that’s petty with leader going, penning personal resignation
- Home I abandon, the ultimate in cruelty and wickedness
- Gross injustice in variable housing – I resign!
Buddy explains!

The straight part
We know that "great injustice" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case great injustice = iniquity.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 INIQUITY mean?
INIQUITY noun- Deviation from what is right; gross injustice, sin, wickedness.
- An act of great injustice or unfairness; a sinful or wicked act; an unconscionable deed.