Apply tax cut by leading lady (8)
I believe the answer is:
exercise
'apply' is the definition.
(exercising is a kind of applying)
'tax cut by leading lady' is the wordplay.
'tax' becomes 'excise' (excise is a kind of tax).
'cut by' means one lot of letters goes inside another.
'leading lady' becomes 'er' (Elizabeth Regina).
'excise' enclosing 'er' is 'EXERCISE'.
(Other definitions for exercise that I've seen before include "keep physically fit" , "worry" , "Keep-fit" , "Train, work out" , "Do it to develop skill or fitness" .)