The most common and most likely answer to this crossword clue is the 8 letter word EXOTERIC
I've seen this crossword clue in The Guardian
E
X
O
T
E
R
I
C
Buddy explains!

The straight part
We know that "It’s suitable in public" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it’s suitable in public = exoteric.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 EXOTERIC mean?
EXOTERIC adjective- Suitable to be imparted to the public without secrecy or other reserves
- (by extension) Accessible; capable of being readily or fully comprehended; or, having an obvious application
- Public or popular; having wide currency
- External