Cut out training with no sign of hesitation (6)
I believe the answer is:
excise
'cut out' is the definition.
(I've seen this in other clues)
'training with no sign of hesitation' is the wordplay.
'training' becomes 'exercise' (exercise is a kind of training).
'with no' indicates named letters should be taken away.
'sign of hesitation' becomes 'er'.
'exercise' with 'er' removed is 'EXCISE'.
(Other definitions for excise that I've seen before include "Internal tax" , "A tax to be cut out, perhaps" , "Duty; cut out" , "Type of tax" , "Customs" .)