Q.Ponytail palm
Ponytail palm seems to be sick. Bark his come loose from trunk. It has a new start or baby on the side. What can I do to save plant? Or can I cut new start and start a new plant?

How is the rest of the plant? Wilting, yellowing or brown leaves?
This could be a fungus or even root rot.
Make sure your watering correctly and that the soil is not soggy.
I would isolate the plant and monitor the situation.
Yes, you can propagate the 'pup' from your plant.
Here are some articles to help you and refresh you on the care requirements.
https://www.gardeningknowhow.com/houseplants/ponytail-palm/ponytail-palm-care.htm
https://www.gardeningknowhow.com/houseplants/ponytail-palm/ponytail-palm-care.htm