The most common and most likely answer to this crossword clue is the 8 letter word CATENARY
C
A
T
E
N
A
R
Y
More clues leading to the result CATENARY
Buddy explains!

The straight part
We know that "Curve" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case curve = catenary.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 CATENARY mean?
CATENARY adjective- Relating to a chain; like a chain.
- Relating to a catena.
- The curve described by a flexible chain or a rope if it is supported at each end and is acted upon only by no other forces than a uniform gravitational force due to its own weight and variations involving additional and non-uniform forces.
- Any physical cable, rope, chain, or other weight-supporting structure taking such geometric shape, as a suspension cable for a bridge or a power-transmission line or an arch for a bridge or roof.
- The curve of an anchor cable from the seabed to the vessel; it should be horizontal at the anchor so as to bury the flukes.
- A cable, the segments of which between supports take a catenary geometric shape, supporting in turn an overhead conductor that provides trains, trams or trolley buses with electricity, or the combination of the conductor, the cable, and supports.