Mother goes to New York a lot (4)
I believe the answer is:
many
'a lot' is the definition.
(many means a lot)
'mother goes to new york' is the wordplay.
'mother' becomes 'ma' (Ma is another word for mother or mum).
'goes to' is a charade indicator (letters next to each other).
'new york' becomes 'ny'.
'ma'+'ny'='MANY'
(Other definitions for many that I've seen before include "A great number" , "Multitudinous" , "Lots" , "legion" , "Numerous" .)