The most common and most likely answer to this crossword clue is the 5 plus 6 letter word BEAUX GESTES
I've seen this crossword clue in Financial Times
B
E
A
U
X
G
E
S
T
E
S
Buddy explains!
The straight part
We know that "acts in a gracious way" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case acts in a gracious way = beaux gestes.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.