The most common and most likely answer to this crossword clue is the 9 letter word TREMBLING
I've seen this crossword clue in The Daily Telegraph
T
R
E
M
B
L
I
N
G
Buddy explains!
The straight part
We know that "Anxious quivering" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case anxious quivering = trembling.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 TREMBLING mean?
TREMBLING verb- To shake, quiver, or vibrate.
- To fear; to be afraid.
- A tremble