Is it written in stone that demagogues must? (7)
I believe the answer is:
agitate
'demagogues must?' is the definition.
I can't judge whether this definition defines the answer.
'is it written in stone' is the wordplay.
'written in' is an insertion indicator.
'stone' becomes 'agate' (agate is a type of stone).
'it' placed inside 'agate' is 'AGITATE'.
'that' is the link.
Can you help me to learn more?
(Other definitions for agitate that I've seen before include "Stir; tie a tag (anag.)" , "Campaign" , "cause trouble" , "Keep moving" , "Upset, disturb the surface of" .)