The most common and most likely answer to this crossword clue is the 10 letter word CHIROMANCY
I've seen this crossword clue in The Daily Telegraph
C
H
I
R
O
M
A
N
C
Y
Buddy explains!
The straight part
We know that "fortune-telling" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fortune-telling = chiromancy.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 CHIROMANCY mean?
CHIROMANCY noun- Divination performed by examining the lines in the palms.