Cast a line outside in conclusion (6)
I believe the answer is:
finish
'conclusion' is the definition.
(I know that conclusion can be written as finish)
'cast a line outside in' is the wordplay.
'cast a line' becomes 'fish' (I am not sure about this - if you are sure you should believe this answer much more).
'outside' indicates putting letters inside.
'fish' going around 'in' is 'FINISH'.
Can you help me to learn more?
(Other definitions for finish that I've seen before include "Come to an end" , "perfection" , "completion" , "Bring to an end" , "Put the final touches to" .)