The most common and most likely answer to this crossword clue is the 5 letter word NIQAB
I've seen this crossword clue in Financial Times
N
I
Q
A
B
More clues leading to the result NIQAB
Buddy explains!

The straight part
We know that "Veil" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case veil = niqab.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 NIQAB mean?
NIQAB noun- A veil which covers the face, worn by some Muslim women as a part of sartorial hijab.