Bagpipe played around middle of alley in New York (3,5)
I believe the answer is:
big apple
'new york' is the definition.
(I've seen this before)
'bagpipe played around middle of alley' is the wordplay.
'played' indicates an anagram.
'around' means one lot of letters goes inside another.
'middle of' means to look at the middle letters.
The middle letter of 'alley' is 'l'.
'bagpipe' is an anagram of 'bigappe'.
'bigappe' going around 'l' is 'BIG APPLE'.
'in' is the link.
(Other definitions for big apple that I've seen before include "Informal name for New York" , "Fruity name for New York" , "NY City nickname" , "New York's slang name" , "Nickname for New York" .)