Heartless Tory managed New York dictatorship (7)
I believe the answer is:
tyranny
'dictatorship' is the definition.
(I know that dictatorship can be written as tyranny)
'heartless tory managed new york' is the wordplay.
'heartless' says to hollow out the word (remove centre letters).
'managed' becomes 'ran' (both can mean organised or was in charge of).
'new york' becomes 'ny'.
'tory' with its centre removed is 'ty'.
'ty'+'ran'+'ny'='TYRANNY'
(Other definitions for tyranny that I've seen before include "Oppressive government" , "Cruel and arbitrary rule" , "Cruel rulers" , "Cruel government" , "Form of despotism" .)