The most common and most likely answer to this crossword clue is the 8 letter word UNSUITED
I've seen this crossword clue in The Daily Telegraph
U
N
S
U
I
T
E
D
Buddy explains!

The straight part
We know that "Inappropriate" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case inappropriate = unsuited.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 UNSUITED mean?
UNSUITED adjective- Not suited to a specific purpose.
- Not compatible; mismatched.
- Not wearing a suit.
- (said of two or more cards) Not of the same suit.