The most common and most likely answer to this crossword clue is the 6 letter word LUXURY
I've seen this crossword clue in The Guardian
L
U
X
U
R
Y
Buddy explains!

The straight part
We know that "extravagance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extravagance = luxury.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 LUXURY mean?
LUXURY noun- Very wealthy and comfortable surroundings.
- Something desirable but expensive.
- Something that is pleasant but not necessary in life.
- Very expensive
- Not essential but desirable and enjoyable and indulgent.
- Pertaining to the top-end market segment for mass production mass market vehicles, above the premium market segment.