The most common and most likely answer to this crossword clue is the 11 letter word ARISTOCRACY
I've seen this crossword clue in The Guardian
A
R
I
S
T
O
C
R
A
C
Y
Buddy explains!

The straight part
We know that "nobs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nobs = aristocracy.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 ARISTOCRACY mean?
ARISTOCRACY noun- The nobility, or the hereditary ruling class.
- Government by such a class, or a state with such a government
- A class of people considered (not normally universally) superior to others