Beastly type turns up to graduate (4)
I believe the answer is:
puma
'beastly type' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'turns up to graduate' is the wordplay.
'turns' says the letters should be written backwards.
'to graduate' becomes 'ma' (abbreviation for Master of Arts).
'up' written backwards gives 'pu'.
'pu'+'ma'='PUMA'
Can you help me to learn more?
(Other definitions for puma that I've seen before include "Cougar" , "American wild cat" , "Large Am. wild cat" , "American wildcat" , "International rugby player" .)