Rent at different rate (4)
I believe the answer is:
tear
'rent' is the definition.
(I know that rent can be written as tear)
'different rate' is the wordplay.
'different' indicates anagramming the letters.
'rate' is an anagram of 'TEAR'.
'at' acts as a link.
(Other definitions for tear that I've seen before include "A rip goes on a binge?" , "Lachrymal fluid" , "Lacerate - sign of sorrow" , "Rip - eye moisture" , "A rip or cut" .)