The most common and most likely answer to this crossword clue is the 6 letter word RIDLEY
I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "Oxford martyr" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case oxford martyr = ridley.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 RIDLEY mean?
RIDLEY noun- Any of the marine turtles of the genus Lepidochelys, found in the Atlantic and Pacific oceans.