Hi & welcome!
If you cut a piece off of the rhizome and half-bury it on the soil surface in the new pot, it should take root & start growing leaves. I would let it dry overnight after cutting, and pot it the next day.
Alternately, you could unpot your plant, cut the rhizome at a spot where both pieces have some roots & leaves. If doing this, I would repot right away, keeping the wound exposed (and as clean as possible) so it can dry, and wait until the following day to water.