In modern times, a girl is greedy (4)
I believe the answer is:
avid
'greedy' is the definition.
(synonyms)
'in modern times a girl' is the wordplay.
'in' indicates putting letters inside.
'modern times' becomes 'AD' (AD, Anno Domini, as opposed to BC, Before Christ).
'a girl' becomes 'Vi' (short for Violet).
'ad' going around 'vi' is 'AVID'.
'is' is the link.
(Other definitions for avid that I've seen before include "Showing a very keen interest in something" , "Extremely keen" , "'Eager, enthusiastic (4)'" , "deeply enthusiastic" , "Keen, enthusiastic" .)