Cryptic crossword clue
Prince is enthralled by marines’ extreme strictness 8

The most common and most likely answer to this crossword clue is the 8 letter word RIGORISM

I've seen this crossword clue in Financial Times
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Buddy explains!

The straight part
We know that "extreme strictness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extreme strictness = rigorism.
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 RIGORISM mean?

RIGORISM noun
  1. Strictness (in interpreting or enforcing a rule)
  2. In Roman Catholic moral theology, the doctrine that in a case of doubt between right and wrong one should take the safer course, i.e. the one in verbal accordance with the law.

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