eg roaring out this chant (9)
I believe the answer is:
gregorian
'chant' is the definition.
(Gregorian chant is an example)
'eg roaring out' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'eg'+'roaring'='egroaring'
'egroaring' anagrammed gives 'GREGORIAN'.
'this' acts as a link.
(Other definitions for gregorian that I've seen before include "Type of calendar, of chant" , "relating to calendar" , "Like sixteen popes" , "Sort of chant" , "maybe chants?" .)