Old woman after plague offers opinion (5)
I believe the answer is:
dogma
'opinion' is the definition.
(dogma means belief)
'old woman after plague' is the wordplay.
'old woman' becomes 'ma' (both can mean someone's mother).
'after' is a charade indicator (letters next to each other).
'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 "Beliefs laid down as incontrovertibly true" , "Body of creed" , "Principles laid down by authority as true" , "Some believe it certainly" , "Code of belief" .)