Girl with land in South America losing capital (6)
I believe the answer is:
olivia
'girl' is the definition.
'land in south america losing capital' is the wordplay.
'land in south america' becomes 'Bolivia' (country in South America).
'losing capital' means to remove the first letter.
'bolivia' with its initial letter removed is 'OLIVIA'.
'with' acts as a link.
(Other definitions for olivia that I've seen before include "- de Havilland, US film actress" , "Woman" , "-- Newton-John, singer" , "Female character in Twelfth Night" , "Countess in Twelfth Night" .)