The most common and most likely answer to this crossword clue is the 4 letter word SCAT
I've seen this crossword clue in The Daily Telegraph
S
C
A
T
More clues leading to the result SCAT
- Go away and sing some jazz
- Droppings from small animal
- Primarily: sing crazily, absent text?
- Go away singing jazz
- Southern Burmese perhaps get lost
- Get away with wordless singing
- Mass caterer’s ingredient to go off quickly
- Beginning to sing, jazz fan may do this
- Improvised performance in musical, back to front
- Leave droppings of carnivore, small one
Buddy explains!

The straight part
We know that "sort of singing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sort of singing = scat.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 SCAT mean?
SCAT noun- A tax; tribute.
- A land-tax paid in the Shetland Islands.
- Animal excrement; droppings, dung.
- Heroin.
- Whiskey.
- Coprophilia.
- A brisk shower of rain, driven by the wind.
- Scat singing.
- To sing an improvised melodic solo using nonsense syllables, often onomatopoeic or imitative of musical instruments.
- To leave quickly (often used in the imperative).
- An imperative demand, often understood by speaker and listener as impertinent.
- Any fish in the family Scatophagidae