New girl? Daughter may be mollycoddled (7)
I believe the answer is:
nannied
'be mollycoddled' is the definition.
(I've seen this before)
'new girl? daughter' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'girl?' becomes 'annie' ().
'daughter' becomes 'd' (genealogical abbreviation).
'n'+'annie'+'d'='NANNIED'
'may' is the link.
(Other definitions for nannied that I've seen before include "wrapped in cotton wool" , "fussed over" , "Mollycoddled" .)