Guy, following extremely anarchic desire, ... (4)
I believe the answer is:
ache
'desire' is the definition.
(ache can mean a passionate desire for something)
'guy following extremely anarchic' is the wordplay.
'guy' becomes 'he' (I can't justify this - if you can you should believe this answer much more).
'following' means one lot of letters go next to another.
'extremely' says to hollow out the word (remove centre letters) (only the extremes of the word are used).
'anarchic' with its centre removed is 'ac'.
'he' after 'ac' is 'ACHE'.
Can you help me to learn more?
(Other definitions for ache that I've seen before include "Throb - hurt" , "Dull throbbing pain" , "Play up" , "Shakespearean character" , "Twinge" .)