The most common and most likely answer to this crossword clue is the 3 plus 3 plus 3 letter word TIE AND DYE
I've seen this crossword clue in Financial Times
T
I
E
A
N
D
D
Y
E
Buddy explains!
The straight part
We know that "a dying art you might say" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a dying art you might say = tie and dye.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.