The most common and most likely answer to this crossword clue is the 8 letter word SEEDIEST
I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "extremely sleazy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extremely sleazy = seediest.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 SEEDIEST mean?
SEEDIEST adjective- Full of seeds.
- Disreputable, run-down.
- Untidy; unkempt.
- Infirm; unwell; gone to seed.
- Suffering the effects of a hangover.
- Having the flavour of seeds.
- Having a peculiar flavour supposed to be derived from the weeds growing among the vines; said of certain kinds of French brandy.