Rent at different rate (4)
I believe the answer is:
tear
'rent' is the definition.
(synonyms)
'different rate' is the wordplay.
'different' is an anagram indicator (letters placed in a different order).
'rate' with letters rearranged gives '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" .)