The most common and most likely answer to this crossword clue is the 12 letter word SKYROCKETING
I've seen this crossword clue in The Daily Telegraph
S
K
Y
R
O
C
K
E
T
I
N
G
Buddy explains!

The straight part
We know that "Fast-rising" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fast-rising = skyrocketing.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 SKYROCKETING mean?
SKYROCKETING verb- To increase suddenly and extremely; to shoot up; to surge or spike.