The most common and most likely answer to this crossword clue is the 10 letter word INTIMATION
I've seen this crossword clue in The Guardian
I
N
T
I
M
A
T
I
O
N
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 = intimation.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 INTIMATION mean?
INTIMATION noun- The act of intimating.
- The thing intimated.
- Announcement; declaration.
- A hint; an obscure or indirect suggestion or notice; a remote or ambiguous reference.