Clue: Island has job getting rid of king — madness ensues (8)
Answer: TASMANIA
Explanation: Definition: Island
 "task"(a job/a piece of work) **minus**(getting rid of) "k"(abbrev. for "king" in chess notation) **placed above**(… ensues, in a down clue) MANIA(madness/mental illness).
Defn: … in Australia.