The most common and most likely answer to this crossword clue is the 15 letter word INTERNATIONALLY
I've seen this crossword clue in The Daily Telegraph
I
N
T
E
R
N
A
T
I
O
N
A
L
L
Y
Buddy explains!
The straight part
We know that "involving many different countries" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case involving many different countries = internationally.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 INTERNATIONALLY mean?
INTERNATIONALLY adverb- In an international manner.