The most common and most likely answer to this crossword clue is the 7 letter word FIGLEAF
I've seen this crossword clue in Financial Times
F
I
G
L
E
A
F
Buddy explains!
The straight part
We know that "Cover-up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cover-up = figleaf.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 FIGLEAF mean?
FIGLEAF noun- A leaf of the fig plant.
- A representation of leaf of a fig plant used to cover the genitals of a nude figure in a work of art (alluding to Genesis iii 7, in which Adam and Eve use fig leaves to hide their nakedness).
- Anything used to conceal something undesirable or that one does not want to be discovered.