Regrettably, Kay's not finished, being in a state (6)
I believe the answer is:
alaska
'a state' is the definition.
(Alaska is a US state)
'regrettably kay's not finished' is the wordplay.
'regrettably' becomes 'alas' ('alas' is said before regrettable news).
'not finished' means to remove the last letter.
'kay' with its last letter removed is 'ka'.
'alas'+'ka'='ALASKA'
'being in' acts as a link.
(Other definitions for alaska that I've seen before include "Anchorage is the largest city" , "Forty-ninth US state" , "that may be baked? Not by the sun" , "NW US state" , "Most northerly state of USA" .)