Fly round state in subjugation (7)
I believe the answer is:
slavery
'subjugation' is the definition.
(slavery is a kind of subjugation)
'fly round state in' is the wordplay.
'fly round' becomes 'sly' (I can't explain this - if you can you should believe this answer much more).
'state' becomes 'aver' (both can mean to declare).
'in' is an insertion indicator.
'sly' going around 'aver' is 'SLAVERY'.
Can you help me to learn more?
(Other definitions for slavery that I've seen before include "State of subjugation" , "Bondage" , "Extreme drudgery" .)