Graduate going to New York a lot (4)
I believe the answer is:
many
'a lot' is the definition.
(many means a lot)
'graduate going to new york' is the wordplay.
'graduate' becomes 'MA' (abbreviation for Master of Arts).
'going to' says to put letters next to each other.
'new york' becomes 'ny'.
'ma'+'ny'='MANY'
(Other definitions for many that I've seen before include "Lots" , "Several" , "Numerous" , "regarded as a large number" , "legion" .)