No, you cannot simply use the Windows 11 Pro product key on another PC after the old system has been decommissioned. Microsoft licences are usually tied to a specific hardware and cannot be easily transferred to other devices.

In order to use the product key on a new PC, the old system would have to be deactivated and the product key released by Microsoft, but this does not happen automatically when the old system is taken out of operation. It is advisable to contact Microsoft support to request the transfer of the licence and ensure that this is permitted under the licence conditions.