Work out tax cut with head of state (8)
I believe the answer is:
exercise
'work out' is the definition.
(synonyms)
'tax cut with head of state' is the wordplay.
'tax' becomes 'excise' (excise is a kind of tax).
'cut with' indicates putting letters inside.
'head of state' becomes 'er' (abbreviation for Elizabeth Regina).
'excise' going around 'er' is 'EXERCISE'.
(Other definitions for exercise that I've seen before include "Healthy activity" , "worry" , "Gym activity?" , "Exertion by 17 across" , "Task for pupil" .)