The most common and most likely answer to this crossword clue is the 6 letter word SENSEI
I've seen this crossword clue in The Times
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More clues leading to the result SENSEI
Buddy explains!

The straight part
We know that "Karate instructor" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case karate instructor = sensei.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 SENSEI mean?
SENSEI noun- A martial arts instructor. Sensei of martial arts usually live and/or work at a dojo where they instruct their apprentices. A live-in apprentice is also called uchi-deshi.
- A Japanese (language) teacher.
- A suffix attached to the name of a teacher (principally in translations from Japanese)