Work out tax cut by the Queen (8)
I believe the answer is:
exercise
'work out' is the definition.
('exercise' can be a synonym of 'work out')
'tax cut by the queen' is the wordplay.
'tax' becomes 'excise' (excise is a kind of tax).
'cut by' is an insertion indicator.
'the queen' becomes 'er' (Elizabeth Regina).
'excise' going around 'er' is 'EXERCISE'.
(Other definitions for exercise that I've seen before include "Exertion to develop endurance or skill" , "Do it to get fit" , "Do it to develop skill or fitness" , "Practice task" , "Task performed to develop skill" .)