Person sought for different crime

New Zealand

New Zealand - International Crimes and International criminal Court Act 2000 (2021) EN

48 Surrender order may take effect at later date
(1) This section applies if the Minister has determined under section 47 that in all other respects it is appropriate to make a surrender order, but the person is liable to be detained in a prison because of a sentence of imprisonment imposed for a different offence against the law of New Zealand.

New Zealand - International War Crimes Tribunal Act 1995 (2021)EN

Effect of surrender on prisoner sentence
(1) Subecjt to subsection (2), where a person who is serving a setnce in respect of an offence against the law of New Zealand is surrendered to a Tribunal, the person shall, while he or she is in the custody of, or on the order of, the TriĀ­bunal (including custody outside New Zealand), be deemed to be continuing to serve that sentence.
(0) If the person is convicted of a Tribunal offence, time spent by the person in custody serving a sentence of imprisonment imposed by the Tribunal for the Tribunal offence is not to be counted as time towards the sentence referred to in subsection (1).

Rome Statute

Article 89 Surrender of persons to the Court

4. If the person sought is being proceeded against or is serving a sentence in the requested State for a crime different from that for which surrender to the Court is sought, the requested State, after making its decision to grant the request, shall consult with the Court.