The most common and most likely answer to this crossword clue is the 9 letter word CURVATURE
I've seen this crossword clue in Financial Times
C
U
R
V
A
T
U
R
E
More clues leading to the result CURVATURE
- Bend rule over V&A replacing lecturer in the arts
- Dog, very old, with head dropped and arching
- Scoundrel’s tax certain to be topped — it’s not on the level!
- Measure of canine velocity — a true function
- Dog’s privates — essentially, true representation of what makes something voluptuous?
- Arch villain very old getting topped
Buddy explains!

The straight part
We know that "Arch" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case arch = curvature.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 CURVATURE mean?
CURVATURE noun- The shape of something curved.
- The extent to which a subspace is curved within a metric space.
- The extent to which a Riemannian manifold is intrinsically curved.