The most common and most likely answer to this crossword clue is the 7 letter word QUADRIC
I've seen this crossword clue in Financial Times
Q
U
A
D
R
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C
Buddy explains!

The straight part
We know that "of the second degree" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of the second degree = quadric.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 QUADRIC mean?
QUADRIC noun- A surface or curve whose shape is defined in terms of a quadratic equation
- Of or relating to the second degree; quadratic.