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 defines the answer.
'is it written in stone' is the wordplay.
'written in' is an insertion indicator.
'stone' becomes 'agate' (I've seen this before).
'it' put into '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" .)