The most common and most likely answer to this crossword clue is the 9 letter word TRUE-BLUE
I've seen this crossword clue in Financial Times
T
R
U
E
-
B
L
U
E
Buddy explains!

The straight part
We know that "Extremely loyal" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extremely loyal = true-blue.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 TRUE-BLUE mean?
TRUE-BLUE adjective- Steadfastly loyal or faithful, unwavering in loyalty.
- Authentic, undoubtedly true; honest.