The most common and most likely answer to this crossword clue is the 8 letter word TAXONOMY
I've seen this crossword clue in The Times
T
A
X
O
N
O
M
Y
More clues leading to the result TAXONOMY
Buddy explains!
The straight part
We know that "Classification" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case classification = taxonomy.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 TAXONOMY mean?
TAXONOMY noun- The science or the technique used to make a classification.
- A classification; especially, a classification in a hierarchical system.
- The science of finding, describing, classifying and naming organisms.