Cryptic crossword clue
  Vice President abruptly hit out over spymaster’s problem-solving method 9

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

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

The straight part
We know that "problem-solving method" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case problem-solving method = algorithm.
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 ALGORITHM mean?

ALGORITHM noun
  1. A collection of ordered steps that solve a mathematical problem. A precise step-by-step plan for a computational procedure that possibly begins with an input value and yields an output value in a finite number of steps.
  2. Calculation with Arabic numerals; algorism.

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