New York district overlooking old shady business (5,6)
I believe the answer is:
dirty tricks
'shady business' is the definition.
'new york district overlooking old' is the wordplay.
'new' is an anagram indicator.
'overlooking' indicates named letters should be taken away.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'york'+'district'='yorkdistrict'
'yorkdistrict' with 'o' taken out is 'yrkdistrict'.
'yrkdistrict' is an anagram of 'DIRTY TRICKS'.
(Other definitions for dirty tricks that I've seen before include "Political intrigues" , "Underhand (business or political) behaviour" , "Shady dealings" , "Filthy tactics?" .)