The most common and most likely answer to this crossword clue is the 7 letter word QUAVERS
I've seen this crossword clue in Financial Times
Q
U
A
V
E
R
S
More clues leading to the result QUAVERS
Buddy explains!

The straight part
We know that "With a trembling voice, sings/notes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case with a trembling voice, sings/notes = quavers.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 QUAVERS mean?
QUAVERS noun- A trembling shake.
- A trembling of the voice, as in speaking or singing.
- An eighth note, drawn as a crotchet (quarter note) with a tail.
- To shake in a trembling manner.
- To use the voice in a trembling manner, as in speaking or singing.
- To utter quaveringly.