Part 3—Requests by the ICC for arrest and surrender of persons
Division 4—Surrender of persons
40 Request from ICC and foreign country relating to different conduct
(1) If a request for surrender of a person is made and a foreign country requests the extradition of the person for conduct other than the conduct that forms the basis of the crime for which the person’s surrender is sought, the Attorney General must determine whether the person is to be surrendered or is to be extradited to the foreign country.
(2) If Australia is not under an international obligation to extradite the person to the foreign country, priority must be given to the request from the ICC.
(3) If Australia is under an international obligation to extradite the person to the foreign country, the Attorney General must determine whether to surrender the person or to extradite the person to the foreign country.
(4) In making the determination under subsection (3), the Attorney General must consider all relevant matters, including, but not limited to, the matters specified in subsection 39(7), but must give special consideration to the relative nature and gravity of the conduct for which surrender and extradition are sought.
Competing request - different conduct
EDIT.