The most common and most likely answer to this crossword clue is the 4 letter word WISP
I've seen this crossword clue in The Times
W
I
S
P
More clues leading to the result WISP
- Thin person’s desire to get parking for husband
- Shred waste in safe place to start with
- Piece of straw is perhaps thus described
- Waster intently seeking pub heads for Strand
- Groom’s bunch of straw — or strap, when this?
- Small thin person is quietly hiding behind wife
- Narrow strand in Western Isles by top of promenade
- Strand which I should pull initially
- Masked fellow is picking lock
Buddy explains!

The straight part
We know that "Shred" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shred = wisp.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 WISP mean?
WISP noun- A small bundle, as of straw or other like substance; any slender, flexible structure or group.
- A whisk, or small broom.
- A will o' the wisp, or ignis fatuus.
- An immeasurable, indefinable essence of life; soul.
- A disease affecting the feet of cattle.
- To brush or dress, as with a wisp.
- To rumple.
- To produce a wisp, as of smoke.