Lack of experience of top-class doctor in New York (7)
I believe the answer is:
naivety
'lack of experience' is the definition.
(I've seen this before)
'top-class doctor in new york' is the wordplay.
'top class' becomes 'ai' (resembles A1, old-fashioned term meaning excellent).
'doctor' becomes 'vet' (vet is a kind of doctor).
'in' means one lot of letters goes inside another.
'new york' becomes 'ny'.
'ai'+'vet'='aivet'
'aivet' put inside 'ny' is 'NAIVETY'.
'of' is the link.
(Other definitions for naivety that I've seen before include "Ingenuousness" , "Lack of sophistication or experience" , "State of innocence or simplicity (7)" , "credulousness" , "Quality of impractical innocence" .)