The most common and most likely answer to this crossword clue is the 8 letter word CAUTIOUS
I've seen this crossword clue in Financial Times
C
A
U
T
I
O
U
S
More clues leading to the result CAUTIOUS
Buddy explains!

The straight part
We know that "Wary" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wary = cautious.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 CAUTIOUS mean?
CAUTIOUS adjective- Careful; using or exercising caution; tentative