Fastest mission to imprison 'illbilly (8)
I believe the answer is:
quickest
'fastest' is the definition.
('quick' can be similar in meaning to 'fast')
'mission to imprison 'illbilly' is the wordplay.
'mission' becomes 'quest' (a quest is a mission or search).
'to imprison' is an insertion indicator.
''illbilly' becomes 'ick' (I can't justify this - if you can you should believe this answer much more).
'quest' going around 'ick' is 'QUICKEST'.
Can you help me to learn more?
(Other definitions for quickest that I've seen before include "First to get there?" , "Speediest" , "Most swift" , "Fastest" .)