From the description you provided, it seems you want to transfer free upgrade license on old computer to new laptop (feel free to correct, if I misunderstood your query).
For that, you need to confirm that old PC had retail license, when you upgraded it to Windows 10 from Windows 7/8.1. Here's how to transfer your license:
In case if old PC had an OEM license, unfortunately you can't transfer the license to your laptop. You'll need to buy new license in that case.
Note: Included link in this reply refers to blog post by a trusted Microsoft MVP.