The most common and most likely answer to this crossword clue is the 10 letter word JET-SETTER
I've seen this crossword clue in Financial Times
J
E
T
-
S
E
T
T
E
R
More clues leading to the result JET-SETTER
Buddy explains!
The straight part
We know that "she gets about in style" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case she gets about in style = jet-setter.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.