Most companies that go through this kind of process will retain the previous infrastructure (in your case netbackup) around for as long as retention requirements dictate and then retire it on the off chance they need to restore that old data. The old system is not retired until the data backed up to it is no longer required for retention. Since most restores are done to restore the most recent copy of data, this generally implies the old system won't be used much, if at all. It's there to satisfy retention requirements.
Depending on how complex your environment is, you may have some portion of your data that involves infinite retention or really long retention requirements. For that data you will indeed have to restore it and re back it up. There is no way to convert from netbackup to TSM as has already been pointed out. This is pretty much the norm though when switching from any backup software to another.