While the process I mentioned does seem to assume that you still have the old TM drive with the folder you have that process should work.

If you have already started a new backup it would probably be best to just save the folder that you have on a drive partition somewhere you can always point TM to it when you need access to the older files. In fact there is some software that has this as one of their selling points. Back-In-Time (Information) Although it assumes you have the TM disk it should work with the folder you have. There is a trial version that could be used to test it.