New York speciality to grate into curd cheese (10)
I believe the answer is:
skyscraper
'new york speciality' is the definition.
(New York has many skyscrapers)
'grate into curd cheese' is the wordplay.
'grate' becomes 'scrape' (synonyms).
'into' is an insertion indicator.
'curd cheese' becomes 'skyr' (type of Icelandic cheese).
'scrape' placed into 'skyr' is 'SKYSCRAPER'.
'to' is the link.
(Other definitions for skyscraper that I've seen before include "tower" , "UN HQ building, say" , "Very high building" , "Lofty city building" , "Multi-storey edifice" .)