Is it possible to take a backup made in one NetBackup environment and take the tape into another NetBackup environment and recover data from the backup?
Yes, you will first have to import the tape in to the new enviornment. As long as you don't write any data to the tape in the new environment you can still use it in the original environment.
All of that tape's information from the previous NBU environment/catalog will be added to the new NBU environment/catalog. If you search for your image in the catalog, it would be as if you took the backup within your new environment.
You also have the option of Recovery without import - it takes time to set up - but once done you can skip the import and do restores as soon as you have the tape at the other site.