Sloth's carrying painful condition to rodents (7)
I believe the answer is:
agoutis
'rodents' is the definition.
(I've seen this before)
'sloth's carrying painful condition' is the wordplay.
'sloth's' becomes 'ai's' (ai is a kind of sloth).
'carrying' indicates putting letters inside.
'painful condition' becomes 'gout'.
'ais' going around 'gout' is 'AGOUTIS'.
'to' is the link.
(Other definitions for agoutis that I've seen before include "Rodents" , "More than one animal" .)