The most common and most likely answer to this crossword clue is the 13 letter word GRANDMASTERLY
I've seen this crossword clue in Financial Times
G
R
A
N
D
M
A
S
T
E
R
L
Y
Buddy explains!
The straight part
We know that "Describes international chess matches we presume" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case describes international chess matches we presume = grandmasterly.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.