The most common and most likely answer to this crossword clue is the 4 letter word HIDE
I've seen this crossword clue in The Times
H
I
D
E
More clues leading to the result HIDE
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 = hide.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 HIDE mean?
HIDE verb- To put (something) in a place where it will be harder to discover or out of sight.
- To put oneself in a place where one will be harder to find or out of sight.
- The skin of an animal.
- The human skin.
- (usually United States) One's own life or personal safety, especially when in peril.
- (mainly British) A covered structure from which hunters, birdwatchers, etc can observe animals without scaring them.
- A secret room for hiding oneself or valuables; a hideaway.
- A covered structure to which a pet animal can retreat, as is recommended for snakes.
- To beat with a whip made from hide.
- A unit of land and tax assessment of varying size, originally as intended to support one household with dependents.