You could let the rootstock grow and then graft another variety onto it later or multiple varieties on each branch. The rootstock will either be male or female and not self pollinating.

I'd replace it. But if you want to let your rootstock grow and then graft to it, know that grafting persimmons is all about timing for best results. Obtain your scions in mid to late winter (there are a number of vendors online, or get from a friend locally), and keep them wrapped or sealed in a plastic baggie in your fridge. They must be kept cold and dormant and not dry out. You could even wrap them with Buddy tape. Then when your rootstock is starting to leaf out in late spring, graft the dormant scion onto your active rootstock. Try to match diameters of the scion to the rootstock branch. I did five cleft grafts that way this spring and all took, whereas I've had failures other times of the year!