Cured patient yearns for animal (5,8)
I believe the answer is:
spiny anteater
'animal' is the definition.
(spiny anteater is a kind of animal)
'cured patient yearns' is the wordplay.
'cured' indicates anagramming the letters.
'patient'+'yearns'='patientyearns'
'patientyearns' is an anagram of 'SPINY ANTEATER'.
'for' acts as a link.
(Other definitions for spiny anteater that I've seen before include "Echidna - entertain a spy (anag)" , "Prickly type" .)