An Act to facilitate compliance by Australia with obligations under the Rome Statute of the International Criminal Court, and for related purposes
Part 4 Other requests by ICC
Division 3—Restrictions on provision of assistance
60 Request from ICC and foreign country relating to different conduct
If Australia is not under an international obligation to comply with the request from the foreign country, priority must be given to the request for cooperation.
Competing request - different conduct - no obligation to extradite
EDIT.