Resign, not working after favourite's taken over (4,4)
I believe the answer is:
step down
'resign' is the definition.
(I know that resign can be written as step down)
'not working after favourite's taken over' is the wordplay.
'not working' becomes 'down' (down can mean broken or not working).
'after' is a charade indicator (letters next to each other).
'favourite's' becomes 'pet's' ('pet' can be a synonym of 'favourite').
'taken over' says the letters should be written in reverse.
'pets' reversed gives 'step'.
'down' after 'step' is 'STEP-DOWN'.
(Other definitions for step down that I've seen before include "decrease in output" , "Withdraw from" , "Gradually reduce - resign" , "Leave office" , "Resign, retire" .)