Finish with conclusion of judge in lawsuit (5)
I believe the answer is:
cease
'finish' is the definition.
('cease' can be a synonym of 'finish')
'conclusion of judge in lawsuit' is the wordplay.
'conclusion of' suggests the final letters.
'in' indicates putting letters inside.
'lawsuit' becomes 'case' ('case' can be a synonym of 'lawsuit').
The final letter of 'judge' is 'e'.
'e' going into 'case' is 'CEASE'.
'with' acts as a link.
(Other definitions for cease that I've seen before include "Stop, give over" , "Political group" , "Culminate" , "Stop, finish" , "Finish, end" .)