The most common and most likely answer to this crossword clue is the 9 letter word OCTILLION
I've seen this crossword clue in The Guardian
O
C
T
I
L
L
I
O
N
More clues leading to the result OCTILLION
- Leading couple in formation dance swapping places an awful lot!
- Company doing volte-face in lively dance number
- Twist at start of lively dance for a very large number
- Very large number getting month off
- Twist at the beginning of dance number
- It's a lot — not even once husband is charged
- Huge amount of work stopping no one company rising
Buddy explains!

The straight part
We know that "Very large number" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very large number = octillion.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.