Q.Ponytail palm
My ponytail palm is getting quite large. I need to start again. No pups have arrived, unless a small, new branch from the base has emerged I don’t know if that’s a pup or just a new branch.

Certified GKH Gardening Expert
True pups typically grow from the base near the soil, and I don't see any of those. But you can also propagate the ponytail palm by cutting off the small side branch on the left of the photo and planting it using the same technique as for pups:
https://www.gardeningknowhow.com/houseplants/ponytail-palm/propagating-ponytail-palm-pups.htm
This is slightly less reliable because the side branch won't have roots yet, but it should still work.