...carrying out death penalty (9)
I believe the answer is:
execution
This clue is a double definition.
'carrying out' is the first definition.
('execution' can be a synonym of 'carrying out')
'death penalty' is the second definition.
('execution' can be a synonym of 'death penalty')
(Other definitions for execution that I've seen before include "Queen of Hearts' order" , "Topping" , "Eg, beheading" , "The carrying out of" , "style of musical performance" .)