The most common and most likely answer to this crossword clue is the 11 letter word DEEP-ROOTED
I've seen this crossword clue in The Times
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Buddy explains!
The straight part
We know that "firmly fixed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case firmly fixed = deep-rooted.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-ROOTED mean?
DEEP-ROOTED adjective- (literally, of a plant) Having deep roots; (of a non-living object) deeply and firmly embedded (in the ground, etc.).
- Firmly established in thought or behaviour and difficult to change.