The most common and most likely answer to this crossword clue is the 5 letter word SHRED
I've seen this crossword clue in The Times
S
H
R
E
D
More clues leading to the result SHRED
- Divided among several people, except for a small amount
- A small amount of extremely smooth wine
- Astute waif initially avoided scrap
- Scrap put right in outhouse
- Bit embarrassed evidently by second husband
- Put under joint ownership? A rejected suggestion
- Actor finally in cast gets smallest part
- Keep quiet on Socialist scrap
- A little bit of wine? Cork it at first
- Perceptive wife cleared out grate
Buddy explains!

The straight part
We know that "suggestion" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suggestion = shred.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 SHRED mean?
SHRED noun- A long, narrow piece cut or torn off; a strip.
- In general, a fragment; a piece; a particle; a very small amount.
- To cut or tear into narrow and long pieces or strips.
- To reduce by a large percentage.
- To lop; to prune; to trim.
- To ride aggressively.
- To drop fat and water weight before a competition.
- To play very fast (especially guitar solos in rock and metal genres).