Vice President abruptly hit out over spymaster’s problem-solving method (9)
I believe the answer is:
algorithm
'method' is the definition.
(thesaurus)
'vice president abruptly hit out over spymaster's problem-solving' is the wordplay.
I cannot quite see how this works, but
an anagram of 'hit' is 'ith' which is located in the answer.
'over' could be 'o' (cricket abbreviation) and 'o' is present in the answer.
'spymaster' could be 'm' (in James Bond) and 'm' is present in the answer.
This may be the basis of clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for algorithm that I've seen before include "Procedure" , "Problem-solving formula" , "Set of rules (for computer) to solve a problem" , "Set of rules for solving problem by computer" , "What, as a rule, helps maths student" .)