Huge graduate, male, with insect (7)
I believe the answer is:
mammoth
'huge' is the definition.
(synonyms)
'graduate male with insect' is the wordplay.
'graduate' becomes 'MA' (abbreviation for Master of Arts).
'male' becomes 'm' (common abbreviation).
'with' says to put letters next to each other.
'insect' becomes 'moth' (moth is a kind of insect).
'ma'+'m'+'moth'='MAMMOTH'
(Other definitions for mammoth that I've seen before include "Prehistoric woolly elephant" , "Immense" , "Large 15 animal" , "Prehistoric beast like hairy elephant" , "Extinct hairy elephant" .)