The most common and most likely answer to this crossword clue is the 5 letter word HELIX
I've seen this crossword clue in Independent
H
E
L
I
X
More clues leading to the result HELIX
Buddy explains!

The straight part
We know that "curlicue" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case curlicue = helix.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 HELIX mean?
HELIX noun- A curve on the surface of a cylinder or cone such that its angle to a plane perpendicular to the axis is constant; the three-dimensional curve seen in a screw or a spiral staircase.
- A small volute under the abacus of a Corinthian capital.
- The incurved rim of the external ear.
- An upside down midair 360° spin in playboating.
- To form or cause to form a helix.