A varied endless century in greed (7)
I believe the answer is:
avarice
'greed' is the definition.
(avarice is a kind of greed)
'a varied endless century in' is the wordplay.
'endless' means to remove the last letter.
'century' becomes 'C' (common abbreviation).
'in' means one lot of letters goes inside another.
'varied' with its last letter taken away is 'varie'.
'varie' enclosing 'c' is 'varice'.
'a'+'varice'='AVARICE'
(Other definitions for avarice that I've seen before include "Rapacity" , "A deadly sin" , "Cupidity" , "excessive desire for wealth" , "Wanting to be rich" .)