The state of a girl I'd embraced (7)
I believe the answer is:
florida
'the state' is the definition.
(US state)
'girl i'd embraced' is the wordplay.
'girl' becomes 'flora' ().
'embraced' is an insertion indicator (inserted letters are embraced).
'flora' placed around 'id' is 'FLORIDA'.
'of a' is the link.
(Other definitions for florida that I've seen before include "American state, capital Tallahassee" , "Everglade State" , "US location" , "Miami's state" , "Everglades state" .)