One minding children of girl in New York (5)
I believe the answer is:
nanny
'one minding children' is the definition.
'girl in new york' is the wordplay.
'girl' becomes 'ann'.
'in' indicates putting letters inside.
'new york' becomes 'ny'.
'ann' put within 'ny' is 'NANNY'.
'of' is the link.
(Other definitions for nanny that I've seen before include "Undue government interference with personal choice?" , "Children's nurse" , "Issue tender" , "eg Mary Poppins" , "Nursemaid" .)