The most common and most likely answer to this crossword clue is the 14 letter word GOVERNMENTALLY
I've seen this crossword clue in The Sunday Telegraph
G
O
V
E
R
N
M
E
N
T
A
L
L
Y
Buddy explains!
The straight part
We know that "how countries are run" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case how countries are run = governmentally.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.