Dare feisty extremists to challenge authority (4)
I believe the answer is:
defy
'dare' is the definition.
(synonyms)
'feisty extremists to challenge authority' is the wordplay.
'extremists' means to remove the middle letters (letters on the extreme ends of the word).
'to' means one lot of letters go next to another (I've seen this in other clues).
'challenge authority' becomes 'de' (I am not sure about this - if you are sure you should believe this answer much more).
'feisty' with its centre taken out is 'fy'.
'fy' after 'de' is 'DEFY'.
Can you help me to learn more?
(Other definitions for defy that I've seen before include "Stand against" , "Brave" , "Openly resist or refuse to obey" , "Disobey boldly and openly" , "Boldly resist (authority, etc)" .)