The SSD you linked is an M.2 SSD. In order to connect it to a computer without an M.2 slot, you would need to purchase an M.2 to PCIe adapter card.
However, given that you're planning to use the SSD to replace your failing hard drive, I'm assuming that you want to use it as a boot device. To my knowledge, NVMe drives are only supported as boot devices on Haswell CPUs or later, and even then, support is very patchy (M.2/NVMe support has only really become stable and standard in the last couple of generations of CPUs). Your motherboard has a LGA1155 socket and H61 chipset, which indicates that you have a Sandy Bridge processor. Additionally, the H61 chipset is the most basic chipset for this generation, and as such would not incorporate any new, experimental or upcoming features. Therefore, it is almost certain that your motherboard will not support an NVMe device for booting.
Although it might be possible to use the NVMe SSD as a secondary drive, I suspect that you will run into many technical issues along the way which may render the SSD incompatiable with your system. I wouldn't recommend going down this route.
Instead of buying an NVMe SSD, I would recommend simply getting a standard 2.5" SATA SSD. The speed difference between a SATA and NVMe SSD is usually not noticable during general use, and only really makes a difference if you are using the drive for read/write heavy workloads (e.g. as a scratch disk for video editing). The money saved from buying a SATA drive would also allow you to buy more storage for the same price. Finally, you are unlikely to run into any compatiability issues with SATA, whilst an NVMe SSD is almost certain to give you grief on older systems.