The most common and most likely answer to this crossword clue is the 11 letter word DEEP-SEATED
I've seen this crossword clue in The Times
D
E
E
P
-
S
E
A
T
E
D
More clues leading to the result DEEP-SEATED
- Firmly-established intense ocean trend regularly observed
- Having gone backward, Spanish car’s finally gone forward – fixed!
- Race over to upset journalist getting entrenched
- Confirmed nickname for Edward, the ocean sailor?
- Edward aboard his bathyscape? It’s in the blood
- Having gone backward, Spanish car's finally gone forward – fixed!
- Fixed the profound article on temperature inside a pit
- Inbred enough not to be on the edge of a chair
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 = deep-seated.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 DEEP-SEATED mean?
DEEP-SEATED adjective- Implanted or firmly established.