The most common and most likely answer to this crossword clue is the 8 letter word WELL-SET
I've seen this crossword clue in Independent
W
E
L
L
-
S
E
T
More clues leading to the result WELL-SET
Buddy explains!

The straight part
We know that "Firmly established" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case firmly established = well-set.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 WELL-SET mean?
WELL-SET adjective- Having a good physical form; strong and symmetrical.
- Firmly established.