Girl comes up with a greeting (3)
I believe the answer is:
ave
'a greeting' is the definition.
(Latin greeting)
'girl comes up' is the wordplay.
'girl' becomes 'Eva' (girl's name).
'comes up' says the letters should be written backwards.
'eva' backwards is 'AVE'.
'with' acts as a link.
(Other definitions for ave that I've seen before include "Roman greeting" , "Hello to the old Romans" , "Hail as to Maria" , "Latin greeting" , "Cockney's own" .)