If that monitor has a cable with a USB-A connector, it is not a 27" Apple Thunderbolt Display. That display uses Thunderbolt as the uplink for its hub ports, so it only has two uplinks: Thunderbolt and power.
That's a good thing in your case, because the 27" Apple Thunderbolt Display (model A1407) will only work with Thunderbolt 1/2 input – not with Mini DisplayPort input. The similar LED Cinema Display (27-inch) – which has a USB uplink – wants Mini DisplayPort input. That's much easier/cheaper to come by.
I believe the power connector on either would be MagSafe 1. There was once an adapter to go from MagSafe 1 to MagSafe 2, but as far as I know, there are no adapters to go from either to MagSafe 3 (the current version). You'll need to power your new MacBook another way.
You will need to connect the USB uplink cable if you want to use any of the downstream USB 2.0 hub ports on the 27" LED Cinema Display, and perhaps also if you want to be able to control the display's brightness.