New rate for rent (4)
I believe the answer is:
tear
'rent' is the definition.
('tear' can be a synonym of 'rent')
'new rate' is the wordplay.
'new' is an anagram indicator.
'rate' with letters rearranged gives 'TEAR'.
'for' is the link.
(Other definitions for tear that I've seen before include "Shred" , "Rip, sever roughly" , "Rend; travel in haste" , "charge" , "Hurry" .)