The most common and most likely answer to this crossword clue is the 11 letter word PARAGLIDING
I've seen this crossword clue in The Times
P
A
R
A
G
L
I
D
I
N
G
Buddy explains!

The straight part
We know that "thrilling sport" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case thrilling sport = paragliding.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 PARAGLIDING mean?
PARAGLIDING verb- To take part in paragliding.
- The sport of gliding with a paraglider.
- The use of a paraglider in other settings, such as surveillance or military applications.