Was the old HDD connected to the system when you did a clean install of Windows to the new HDD? If so, and if the old drive fails or you take it out or reformat it, Windows MAY not boot, as the Windows install could have written some boot files to the old HDD. You may want to test that out now by powering down the computer, disconnecting the old HDD's SATA cable, and then power the computer back on. If it boots into Windows, you are fine, but if it doesn't, at least you will now rather than later.
And doing what elbert suggested makes sense, but with any storage device, have anything important backed up is a good practice.