Vice beginning to increase in New York — I'm going! (8)
I believe the answer is:
iniquity
'vice' is the definition.
(thesaurus)
'beginning to increase in new york i'm going' is the wordplay.
'beginning to' indicates taking the first letters.
'in' is an insertion indicator.
'new york' becomes 'ny'.
'i'm going' becomes 'iquit' ('I quit' might be said by someone leaving).
The initial letter of 'increase' is 'i'.
'ny' placed around 'iquit' is 'niquity'.
'i'+'niquity'='INIQUITY'
(Other definitions for iniquity that I've seen before include "Going wrong" , "Evil act" , "Gross injustice; crime" , "Lack of justice" , "Great wickedness or injustice" .)