Arrest nation's number one baseless conspiracy theorist (4)
I believe the answer is:
nick
'arrest' is the definition.
(I've seen this before)
'nation's number one baseless conspiracy theorist' is the wordplay.
'nation's number one' becomes 'n' (ist letter of 'nation').
'baseless conspiracy theorist' becomes 'ick' (I can't explain this - if you can you should give a lot more credence to this answer).
'n'+'ick'='NICK'
Can you help me to learn more?
(Other definitions for nick that I've seen before include "Prison - steal" , "Slammer - swipe" , "Cut; steal (colloq.)" , "Clink" , "Small cut - if old, the devil" .)