Following acting in New York, Sly brings chaos (7)
I believe the answer is:
anarchy
'chaos' is the definition.
(I've seen this in another clue)
'following acting in new york sly' is the wordplay.
'following' means one lot of letters go next to another.
'acting' becomes 'a' (abbreviation, eg in job titles).
'in' means one lot of letters goes inside another.
'new york' becomes 'ny'.
'sly' becomes 'arch' (I've seen this before).
'ny' going around 'arch' is 'narchy'.
'a' put next to 'narchy' is 'ANARCHY'.
'brings' is the link.
(Other definitions for anarchy that I've seen before include "Collapse of order, rule" , "Chaotic state" , "Lawlessness; chaos" , "Absence of government" , "Complete absence of law" .)