The most common and most likely answer to this crossword clue is the 8 letter word INKLINGS
I've seen this crossword clue in The Guardian
I
N
K
L
I
N
G
S
Buddy explains!

The straight part
We know that "Suspicions" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suspicions = inklings.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 INKLINGS mean?
INKLINGS noun- Usually preceded by forms of to give: a slight hint, implication, or suggestion given.
- Often preceded by forms of to get or to have: an imprecise idea or slight knowledge of something; a suspicion.
- A desire, an inclination.