Cryptic crossword clue
Vice unit working to apprehend Duke following certain reasoning 9

The most common and most likely answer to this crossword clue is the 9 letter word INDUCTIVE

I've seen this crossword clue in Independent
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Buddy explains!

The straight part
We know that "following certain reasoning" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case following certain reasoning = inductive.
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.

Crossword Answer definitions

INDUCTIVE adjective
  1. Of, or relating to logical induction.
  2. Of, relating to, or arising from inductance.
  3. Introductory or preparatory.
  4. Influencing; tending to induce or cause.

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