Girl in the morning leaving US (5)
I believe the answer is:
erica
'girl' is the definition.
'morning leaving us' is the wordplay.
'morning' becomes 'am' (as in 12:00 AM).
'leaving' is a deletion indicator.
'us' becomes 'America' (synonyms).
'america' with 'am' taken away is 'ERICA'.
'in the' acts as a link.
(Other definitions for erica that I've seen before include "Heathland shrub; girl's name" , "Heather's Latin name?" , "Moorland plant, girl's name" , "Girl - heather" , "Shrub genus; girl's name" .)