Your PC has a UEFI BIOS so, yes the AMD RX 480 8GB GPU should be compatible. You will need to measure to find the available space for the double slot wide card.
It is unfortunate that you have only identified the video card with the generic name. Which one is it?
https://www.newegg.com/Product/ProductList.aspx?Submit=ENE&DEPA=0&Order=BESTMATCH&Description=+AMD+R...
You are likely to need to update the PSU to one that is capable of at least 400 W. That depends on which of the two optional PSUs is installed in your PC. It could be 280W or 400W.
The PSU will also need to have a few PCIe power connectors for the card.
I cannot specifically say how many or what type because you gave only a generic identification of the video card upgrade candidate. A brand and model identification would be more specific. There will be at least one eight-pin PCIe power connector required.

I am not an HP Employee.