The most common and most likely answer to this crossword clue is the 8 letter word SERENEST
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The straight part
We know that "Extremely cool" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extremely cool = serenest.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 SERENEST mean?
SERENEST adjective- Peaceful, calm, unruffled.
- Without worry or anxiety; unaffected by disturbance.
- Fair and unclouded (as of the sky); clear; unobscured.
- Used as part of certain titles, originally to indicate sovereignty or independence.