The most common and most likely answer to this crossword clue is the 9 letter word GRADATION
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More clues leading to the result GRADATION
Buddy explains!

The straight part
We know that "degree" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case degree = gradation.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 GRADATION mean?
GRADATION noun- A sequence of gradual, successive stages; a systematic progression.
- A passing by small degrees from one tone or shade, as of color, to another.
- The act of gradating or arranging in grades.
- Any degree or relative position in an order or series.
- A calibration marking.
- A gradual change within one parameter, or an overlapping of two blocks of sound.
- A diatonic succession of chords.
- Apophony.
- To form with gradations.