Do it properly: recover the key then install Windows 10.
To recover the key from your existing Windows installation you can use tools like KeyFinder (https://www.magicaljellybean.com/keyfinder/). This is a legitimate tool to use since you own the Windows 10 licence as you purchased that with your laptop.
Then download Windows 10 from Microsoft's official site. https://www.microsoft.com/software-download/windows10
This will let you do a clean install of Windows 10 to the new hard drive.
You'll need to make a backup of the "old" drive before proceeding with any of this. After Windows 10 has installed on the new drive, copy back any files you want to keep from the backup (whilst ignoring any files you no longer want).
This is the cleanest solution because you're installing a fresh copy of Windows on to a new drive, whilst being able to keep any data you still want afterwards. The advantage of this is it will clean out any stuff you no longer need, which is quite likely to be the case depending on how long you'd had the previous installation. Generally speaking there will be a performance improvement due to this, although the specification of the new versus old drive (e.g SSD vs spinning platter HDD) will be the biggest factor.
This is also one of the most traditional methods when upgrading a drive (clean install of the OS using an existing licence key). People have been doing it since Windows 3.x days. The only difference is that they would typically have a printed copy of the licence key; you're using software to recover it from your current installation. But the end result is much the same.