I decided to get the Modwright upgrade to my HAP Z1ES, and I had them install the SSD. So, I can't help you. Sorry. I can speak in general terms.
The HDD native to the HAP will look nearly identical to the one you bought.
HDDs are usually mounted in fitted racks with (I think) four screws on each rail (that is, each side). The screws go through the rail into threaded holes in the HDD case. The drive will have a ganged connector for power and another for the data bus. Unplug these first. Do this only with the HAP powered off AND unplugged. Remove the screws in the rail and the HDD will slide out easily. Note how it was oriented in the anchor rack and orient the SSD the same. Plug in the connectors, being sure they're properly seated, and slide the SSD in the rack until the mounting holes align. You want the screws tight, as vibration will degrade the performance of the drive.
Again, that's how it works inside a computer; I'm assuming the HAP is the same, but I've never seen the innards of the HAP myself.
If you live near an audiophile retailer, you may be able to get advice from someone there. Remember, these things are assembled by people working cheap. If they can do it, you can too.
Sorry I can't be more helpful.