If you are hoping that adding the ZP will make your soap work as a dandruff shampoo, please know that most people cannot use bar soap to wash their hair. I'm actually one of the few who can, but for most people, it ruins their hair.
Aside from that issue, there is no way of knowing whether or how the ZP would react with the lye used to make soap. Many if not most ingredients are affected by lye. Consider making a syndet bar, which looks like soap, but is actually a solid shampoo with lower pH, that does not require lye to create. That would probably be a better use for this ingredient if you are hoping that it will be effective against dandruff, foot fungus, etc.
If you do go that route, hopefully the supplier can provide the appropriate usage rate, as ZP is very harmful to humans if used in excess of the recommended amount for whatever product you create.