Girl of the Emerald Isle leaving hospital (4)
I believe the answer is:
iris
'girl' is the definition.
(girl's name)
'of the emerald isle leaving hospital' is the wordplay.
'of the emerald isle' becomes 'Irish' (the Emerald Isle is a name for Ireland).
'leaving' is a deletion indicator.
'hospital' becomes 'h' (abbreviation for hospital on maps).
'irish' with 'h' taken away is 'IRIS'.
(Other definitions for iris that I've seen before include "may open up in camera" , "- - Murdoch, novelist" , "Bright flower or eye part" , "Fleur-de-lis" , "Ms Murdoch" .)