Inform on these local extremists (4)
I believe the answer is:
tell
'inform' is the definition.
(telling is a kind of informing)
'on these local extremists' is the wordplay.
'on' means one lot of letters go next to another.
'these' becomes 'te' (I can't justify this - if you can you should believe this answer much more).
'extremists' says to hollow out the word (remove centre letters).
'local' with its centre taken out is 'll'.
'te' put next to 'll' is 'TELL'.
(Other definitions for tell that I've seen before include "blow the whistle" , "Inform - count - Swiss hero" , "Reveal - command" , "Count - give an account" , "Issue instructions" .)