The most common and most likely answer to this crossword clue is the 7 letter word TALLITH
I've seen this crossword clue in The Guardian
T
A
L
L
I
T
H
Buddy explains!

The straight part
We know that "shawl" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shawl = tallith.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 TALLITH mean?
TALLITH noun- A traditional Jewish prayer shawl with tassels which covers the chest and upper part of the back.