The most common and most likely answer to this crossword clue is the 8 letter word OSSIFIED
I've seen this crossword clue in The Daily Telegraph
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Buddy explains!
The straight part
We know that "rigidly set in ways" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rigidly set in ways = ossified.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 OSSIFIED mean?
OSSIFIED adjective- Having undergone the process of ossification (transformation into bone).
- (of ideas or attitudes) Inflexible, old-fashioned.
- Drunk
- To transform (or cause to transform) from a softer animal substance into bone; particularly the processes of growth in humans and animals.
- (animate) To become (or cause to become) inflexible and rigid in habits or opinions.
- (inanimate) To grow (or cause to grow) formulaic and permanent.
- To calcify.