Rent at new rate (4)
I believe the answer is:
tear
'rent' is the definition.
(I know that rent can be written as tear)
'new rate' is the wordplay.
'new' indicates an anagram.
'rate' is an anagram of 'TEAR'.
'at' acts as a link.
(Other definitions for tear that I've seen before include "Rend; travel in haste" , "A globule of eye moisture" , "A rip or cut" , "A rip goes on a binge?" , "Rate (anag.)" .)