Furry animal, shy, with a lead twisted round (5)
I believe the answer is:
coypu
'furry animal' is the definition.
'coypu' can be an answer for 'animal' (coypu is a kind of animal). I am not sure about the 'furry' bit.
'shy with a lead twisted round' is the wordplay.
I cannot quite understand how this works, but
'shy' could be 'coy' (coy can mean shy or modest) and 'coy' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for coypu that I've seen before include "rodents" , "aquatic mammal" , "South American rodent bred for its fur, nutria" , "South American beaver-like beast" , "Animal -- source of nutria fur" .)