Cut out PE without a sign of hesitation (6)
I believe the answer is:
excise
'cut out' is the definition.
(excise can mean to cut out or remove)
'pe without a sign of hesitation' is the wordplay.
'pe' becomes 'exercise' (PE is physical education).
'without' indicates named letters should be taken away.
'a sign of hesitation' becomes 'er'.
'exercise' with 'er' taken away is 'EXCISE'.
(Other definitions for excise that I've seen before include "A tax to be cut out, perhaps" , "Internal tax" , "that wretches hatefully collect" , "Duty; cut out" , "Cut out; commodity tax" .)