Buyout involving Kate possibly finished (8)
I believe the answer is:
takeover
'buyout' is the definition.
(takeover is a kind of buyout)
'kate possibly finished' is the wordplay.
'possibly' indicates anagramming the letters.
'finished' becomes 'over' (similar in meaning).
'kate' with letters rearranged gives 'take'.
'take'+'over'='TAKEOVER'
'involving' acts as a link.
(Other definitions for takeover that I've seen before include "Business deal" , "business manoeuvre" , "Assume control" .)