Does this (connector labeled "SS" below) look like the cable you are using now with the backup drive? DO you have a connection to the drive that looks like the "SS" connector on the left in this image?

If so, the cable shown would connect between the backup drive [left connector]and your new Mac (right connector, USB-C). That cable is called a USB-C to Micro USB 3.1 Gen 2. (The naming is confusing.)
If your backup drive uses a connector like that shown on the left below, then the cable below would be what you need.

USB-C to USB A 3.1 Gen 2. Left connector would go to the backup drive, right connector would go to the new Mac.
This cables or adaptors are inexpensive, maybe $5 or $10.
If in doubt, go to an Apple Store, or an Apple Authorized Service Provider, or places like Best Buy, Staples, large technology stores, etc. What you need for your new Mac is the USB-C, which is on the right in both images above. Bring your backup drive to the store to make sure the other end is the right type for your drive.