The most common and most likely answer to this crossword clue is the 5 plus 5 letter word UPPER CLASS
I've seen this crossword clue in The Daily Telegraph
U
P
P
E
R
C
L
A
S
S
More clues leading to the result UPPER CLASS
Buddy explains!

The straight part
We know that "Aristocratic/sixth form" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case aristocratic/sixth form = upper class.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 UPPER CLASS mean?
UPPER CLASS adjective- Of high social position
- Aristocratic