Training cut without hesitation (8)
I believe the answer is:
exercise
'training' is the definition.
(I know that exercise is a type of military education)
'cut without hesitation' is the wordplay.
'cut' becomes 'excise' (I've seen this in other clues).
'without' indicates putting letters inside ('without' can be similar in meaning to 'outside').
'hesitation' becomes 'er' (sound used when hesitating).
'excise' enclosing 'er' is 'EXERCISE'.
(Other definitions for exercise that I've seen before include "Gym activity?" , "Task performed to develop skill" , "Workout" , "Practice piece of work" , "Do it to develop skill or fitness" .)