The most common and most likely answer to this crossword clue is the 9 letter word GRADUALLY
I've seen this crossword clue in Independent
G
R
A
D
U
A
L
L
Y
More clues leading to the result GRADUALLY
Buddy explains!
The straight part
We know that "by degrees" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case by degrees = gradually.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 GRADUALLY mean?
GRADUALLY adverb- In a gradual manner; making slow progress; slowly.
- By degrees