Business of mature couple's opening in New York (6)
I believe the answer is:
agency
'business' is the definition.
(I know that agency is a type of business)
'mature couple's opening in new york' is the wordplay.
'mature' becomes 'age' (synonyms).
'opening' indicates taking the first letters.
'in' means one lot of letters goes inside another.
'new york' becomes 'ny'.
The first letter of 'couples' is 'c'.
'c' put inside 'ny' is 'ncy'.
'age'+'ncy'='AGENCY'
'of' is the link.
(Other definitions for agency that I've seen before include "Organisation; intervention" , "Bureau; instrumentality" , "Business organisation" , "Government office" , "Business that acts for actors" .)