Who may issue a repreice to delay a person's punishment until a higher cort can hear the case?

Answer:
there is a motion available to allow the defendant to remain on bail until the case is heard by the appellate. in reality - almost an impossible venture in state court, sometimes doable in federal court.
you have to bear in mind that a court judgment is valid until overturned or modified which (truly) does not happen all that often.
so as to your question who can issue a reprieve - the trial court can make the order.
i hope this answers it.

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