The most common and most likely answer to this crossword clue is the 7 letter word ROUNDED
I've seen this crossword clue in The Daily Telegraph
R
O
U
N
D
E
D
Buddy explains!

The straight part
We know that "Curved" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case curved = rounded.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 ROUNDED mean?
ROUNDED verb- To shape something into a curve.
- To become shaped into a curve.
- (with "out") To finish; to complete; to fill out.
- To approximate a number, especially a decimal number by the closest whole number.
- To turn past a boundary.
- To turn and attack someone or something (used with on).
- To advance to home plate.
- To go round, pass, go past.
- To encircle; to encompass.
- To grow round or full; hence, to attain to fullness, completeness, or perfection.
- To do ward rounds.
- To go round, as a guard; to make the rounds.
- To go or turn round; to wheel about.
- To speak in a low tone; whisper; speak secretly; take counsel.
- To address or speak to in a whisper, utter in a whisper.
- Made into a circle or sphere.
- Complete or balanced.
- Describing a number that has been changed to its nearest desired value.
- Ending in a broad arch.
- (of a vowel etc.) Pronounced with the lips drawn together.