Work out duty to protect the Queen (8)
I believe the answer is:
exercise
'work out' is the definition.
('exercise' can be a synonym of 'work out')
'duty to protect the queen' is the wordplay.
'duty' becomes 'excise' (I've seen this before).
'to protect' is an insertion indicator.
'the queen' becomes 'er' (Elizabeth Regina).
'excise' placed around 'er' is 'EXERCISE'.
(Other definitions for exercise that I've seen before include "Practice task" , "Train, work out" , "Exertion to develop fitness" , "Physical training or exertion" , "Exertion to develop endurance or skill" .)