Rent at terrible rate (4)
I believe the answer is:
tear
'rent' is the definition.
(I know that rent can be written as tear)
'terrible rate' is the wordplay.
'terrible' is an anagram indicator.
'rate' is an anagram of 'TEAR'.
'at' acts as a link.
(Other definitions for tear that I've seen before include "charge" , "Dash; drop" , "Droplet from the eye" , "speed" , "Split - career" .)