Ok, if the PSU does not have the necessary connections/cables it's always best to change it.
The brand model and capacity of PSUs on various rails are usually printed on the sticker on them. If you open the case you can probably see it.
Anyway you need a good 400W PSU and this is a good one with a good price:
https://www.newegg.com/Product/Product.aspx?Item=N82E16817139146&cm_re=CX450M-_-17-139-146-_-Product
It has 2 6+2 PCIE power connectors and over 400W on the 12 volts rail.
However, the HP website says the motherboard is an Intel H61 chipset some H61 motherboards have problems with 10 series nvidia GPUs and are not really compatible. Also the website says it has 4GB RAM by default which is not quite enough for OS and gaming. The PSU is listed as having 220 W which is not enough for a 1060 which needs an 8-pin plus the system. That's kind of cutting it too close.
https://support.hp.com/ie-en/document/c03791266
I think you have to make sure whether the motherboard can run the graphics card (maybe asking HP support) and if you plan to game with the system get a good model PSU from a reliable brand like the one I posted and also increase RAM to 8GB which is enough for almost all games currently.