The most common and most likely answer to this crossword clue is the 4 letter word COSY
I've seen this crossword clue in The Daily Telegraph
C
O
S
Y
More clues leading to the result COSY
- Comfortable with trigonometrical expression
- Leaves Billericay at last — perhaps Ceylon’s warmer?
- Modest about snookers ultimately providing cover for pot
- Cover mathematical function of variable
- One’s comfortably settled over tea
- Safe to get a modest box for the spade
- Warm club closing early on fourth of July
- Intimate function, close to capacity
Buddy explains!

The straight part
We know that "Cover" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cover = cosy.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 COSY mean?
COSY noun- A padded or knit covering put on an item to keep it warm, especially a teapot or egg.
- A padded or knit covering for any item (often an electronic device such as a laptop computer).
- A work of crime fiction in which sex and violence are downplayed or treated humorously, and the crime and detection take place in a small, socially intimate community.
- To become snug and comfortable.
- To become friendly with.
- Affording comfort and warmth; snug; social