Recovery would take long regardless of the media (tape/disk). The catalog contains a lot of tiny files which neither backup nor restore very quickly.
You recently asked about open dedupe in another post. I'm still interested to see what you're not using MSDP?
With that you could establish AIR to your DR site and your catalog would be available when ever you need it, no need for a catalog restore.
Please give us more details about your env.
@FlyMountain BasicDisk Storage Unit can help if you don't want to wait for Tape mounts & its Drive configuration. Make sure you have enough space on your local or SAN disk to create this BasicDisk storage. Keep an additional copy of the Catalog on Tape as well.
While recovering, the recovery file should recognize the storage location (make sure to create a BasicDisk storage unit before you start this process) and restore process will recognize the Catalog Backup. You should test and plan your recovery.
I have recovered by creating BasicStorage Unit on NFS, my catalog size was relatively less to yours and I manged to make sure enough time is available.
The fast and realible way to recovery a backup environment is make images copies using AIR between NetBackup domains.
You can keep a copy of the catalog on disk, taking a snapshot or something similar, or even copying the db/images data and dump from the EMM database, however the NetBackup recovery process is not automatic, it needs manual intervention, but it can be faster than retrieving the catalog from tapes. Some times I use this method to migrate catalogs from one server to another with minimal downtime.
When you need to restore that much of data quickly you'd think availability rather than DR so perhaps a cluster and/or replication could be an option. Generally speaking, a restore of catalog would need a lot of small files to be restored which is not an easy task logically for the file system and it may not be the easiest problem to solve. With 3TB in the catalog you might think of a domain split or replication. There are cheap solutions to replicate the catalog without a cluster if you are willing to do extra steps for restore/failover.
Many people in this thread suggesting AIR, this could be a valid option for future backups, however, if you have 3TB in the catalog, you might have quite a bit on tape storage with long retention for whose images AIR would not help at all. Also if copy of the policy database is also critical (and sometimes it is), AIR wouldn't help either.