The most common and most likely answer to this crossword clue is the 8 letter word TREBLING
I've seen this crossword clue in The Times
T
R
E
B
L
I
N
G
Buddy explains!

The straight part
We know that "fast accumulating" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fast accumulating = trebling.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 TREBLING mean?
TREBLING verb- To multiply by three; to make into three parts, layers, or thrice the amount.
- To become multiplied by three or increased threefold.
- To make a shrill or high-pitched noise.
- To utter in a treble key; to whine.