The most common and most likely answer to this crossword clue is the 8 letter word ORTHODOX
I've seen this crossword clue in The Times
O
R
T
H
O
D
O
X
More clues leading to the result ORTHODOX
- Established novelist makes short broadcast
- Conservative PM once lacking leadership, old Con cross
- Established Pole, losing head, has taken harmful amount neat
- . Conventional hot rod customised to break circuit times
- Steer without crashing hot-rod, as is customary
- Conformist Dorothy endlessly trained to slice beef
- Steer behind modified hot rod, following usual practice
- Conventional old hot rod smashed times
- Men admitting first note on cross is sound
- Thor’s strange god with neat sound in doctrine
Buddy explains!

The straight part
We know that "Established" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case established = orthodox.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 ORTHODOX mean?
ORTHODOX adjective- Conforming to the accepted, established, or traditional doctrines of a given faith, religion, or ideology.
- Adhering to whatever is customary, traditional, or generally accepted.
- Of pollen, seed, or spores: viable for a long time; viable when dried to low moisture content.