Physical activity cut out without hesitation (8)
I believe the answer is:
exercise
'physical activity' is the definition.
(I've seen this before)
'cut out without hesitation' is the wordplay.
'cut out' becomes 'excise' (I've seen this before).
'without' means one lot of letters goes inside another ('without' can be similar in meaning to 'outside').
'hesitation' becomes 'er'.
'excise' going around 'er' is 'EXERCISE'.
(Other definitions for exercise that I've seen before include "Employment" , "Exertion to develop endurance or skill" , "Task performed to develop skill" , "written school task" , "Healthy activity" .)