The most common and most likely answer to this crossword clue is the 8 letter word BEHAVING
I've seen this crossword clue in Financial Times
B
E
H
A
V
I
N
G
Buddy explains!
The straight part
We know that "obedient" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obedient = behaving.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 BEHAVING mean?
BEHAVING verb- To conduct (oneself) well, or in a given way.
- To act, conduct oneself in a specific manner; used with an adverbial of manner.
- To conduct, manage, regulate (something).
- To act in a polite or proper way.
- Behaviour