ArcGIS Pro 2.2 was retired in July 2021. Currently, our university is in the process of license renewal. After the renewal process is done, can MyESRI.com generate a provisioning file (concurrent license) for a retired product such as (ArcGIS Pro 2.2)? If not, can I request it from ESRI?
You could install ArcGIS License Manager 2021.0, and authorize the latest ArcGIS Pro license(s). You should still be able to fetch the license from ArcGIS Pro 2.2 and work with it.
* I would highly recommend you to upgrade ArcGIS Pro to the latest version as well, to avail the latest functionalities (unless there is a business need).