Backup of Time Machine Backup?

Hi, I had a Time Machine backup of my Macbook that I didn't want to continue to update (There were some files that I couldn't successfully recover) and I bought a new hard drive to use as a Time Machine. There were some old files on there that I didn't want Time Machine to potentially wipe out (From one year before the last backup). Can I just link the new hard drive as a new Time Machine and in the future I could always connect the old drive and still be able to access the previous old backup of the time machine? When I first tried to link a new drive, the Mac warned me that it would use both drives and alternate between them for the backup. However I do not want the old drive to ever update anymore and only the new drive to update and make backups. Thank you ahead.