Rent at unusual rate (4)
I believe the answer is:
tear
'rent' is the definition.
(I know that rent can be written as tear)
'unusual rate' is the wordplay.
'unusual' is an anagram indicator.
'rate' anagrammed gives 'TEAR'.
'at' acts as a link.
(Other definitions for tear that I've seen before include "Drop secreted by the lacrimal glands" , "Rip; salty drop" , "Rip or lacerate" , "Lachrymal drop - rip" , "Lachrymal fluid" .)