Graduate after plague offers opinion (5)
I believe the answer is:
dogma
'opinion' is the definition.
(dogma means belief)
'graduate after plague' is the wordplay.
'graduate' becomes 'MA' (abbreviation for Master of Arts).
'after' means one lot of letters go next to another.
'plague' becomes 'dog' (both can mean to follow or repeatedly torment).
'ma' put after 'dog' is 'DOGMA'.
'offers' is the link.
(Other definitions for dogma that I've seen before include "Tenet" , "Settled opinion" , "Principles laid down by authority as true" , "fixed opinion" , "church teaching" .)