Resolve core protest by speaking (6)
I believe the answer is:
orally
'resolve core protest by speaking' is the definition.
I can't judge whether this definition defines the answer.
'resolve core protest by' is the wordplay.
'core' says to take the centre.
'protest by' becomes 'rally' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The middle letter of 'resolve' is 'o'.
'o'+'rally'='ORALLY'
Can you help me to learn more?
(Other definitions for orally that I've seen before include "By (word of) mouth" , "via the trap" , "as auditions are done" , "given drugs thus?" , "How anyone would speak" .)