Busy, and furious dismissing Republican for good (7)
I believe the answer is:
engaged
'busy' is the definition.
(I know that busy can be written as engaged)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for engaged that I've seen before include "Bethrothed" , "Given a ring" , "Preoccupied" , "Hired; busy" , "Took on" .)