Clone Time machine back up onto a new drive?

I am trying to troubleshoot a new Mac. Before, I had two back ups of all my data: on the hard drive of my old iMac and on my external time machine backup drive. Long story, but during a troubleshooting process with the aid of AppleCare support, my iMac was erased. Now I have only the external Time Machine backup.

I bought a new, external backup drive for Time Machine on my new Mac. I am very very afraid of something bad happening to my old Time Machine backup during this troubleshooting process. My question is, is there a way to clone the back up from my old time machine drive to the new one so I once again have two copies? If anything happens to my old time machine back up during this troubleshooting process, I will lose all my files.