Animal completely over graduate (5)
I believe the answer is:
llama
'animal' is the definition.
(I've seen this before)
'completely over graduate' is the wordplay.
'completely' becomes 'all' (synonyms).
'over' says the letters should be written in reverse.
'graduate' becomes 'MA' (abbreviation for Master of Arts).
'all' back-to-front is 'lla'.
'lla'+'ma'='LLAMA'
(Other definitions for llama that I've seen before include "Camel-like animal" , "Woolly Andean animal" , "wool supplier" , "woolly customer" , "one that ruminates" .)