The most common and most likely answer to this crossword clue is the 8 letter word BURNOOSE
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Buddy explains!
The straight part
We know that "Cloak" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cloak = burnoose.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 BURNOOSE mean?
BURNOOSE noun- A thick hooded cloak worn by Berbers and Arabs in Northwest Africa.