The most common and most likely answer to this crossword clue is the 10 letter word SHUDDERING
I've seen this crossword clue in The Times
S
H
U
D
D
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G
Buddy explains!

The straight part
We know that "all of a quiver" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case all of a quiver = shuddering.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 SHUDDERING mean?
SHUDDERING verb- To shake nervously, often from fear or horror.
- To vibrate jerkily.
- An extended or continuous shudder.