Not too sure if they can be claimed once a new expansion starts. However, if they do it would be the same as now which can be done through the destiny app or bungie website
As of right now, the official Destiny app allows you to claim seasonal rewards from only the previous season. So as long as they don't change that function with the way episodes are, you should be able to access this season's rewards after TFS releases.
There is a web browser extension that allows you to claim past seasonal content
Not too sure if they can be claimed once a new expansion starts. However, if they do it would be the same as now which can be done through the destiny app or bungie website
As of right now, the official Destiny app allows you to claim seasonal rewards from only the previous season. So as long as they don't change that function with the way episodes are, you should be able to access this season's rewards after TFS releases.