The most common and most likely answer to this crossword clue is the 9 plus 6 letter word ANTARCTIC CIRCLE
I've seen this crossword clue in The Guardian
A
N
T
A
R
C
T
I
C
C
I
R
C
L
E
More clues leading to the result ANTARCTIC CIRCLE
Buddy explains!
The straight part
We know that "Ring up the world? Quite the opposite" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ring up the world? quite the opposite = antarctic circle.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.