The most common and most likely answer to this crossword clue is the 11 letter word BOURGEOUSIE
I've seen this crossword clue in The Times
B
O
U
R
G
E
O
U
S
I
E
Buddy explains!
The straight part
We know that "conservative classes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case conservative classes = bourgeousie.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.