Is the Finder configured to show mounted volumes on the Desktop or in the sidebar?
If the drive did not mount, then launch Disk Utility. Select your drive/volume in the left pane and click "Mount" or "Unlock". macOS does not always mount external drives automatically especially ones which are using Filevault.
If you launch the Apple System Profiler and check under USB devices, do you see the enclosure listed or the drive? Launch the Apple System Profiler by Option-clicking on the Apple menu and selecting the first option.
Double-check all the connections and reseat everything.
If this doesn't work, then several things are possible:
- Hard drive is bad
- USB Cable is bad
- Enclosure is bad
- Drive isn't getting enough power from the new laptop (try using a powered USB3 hub).
You can check these things by trying to connect the drive to yet another computer. Even a Windows PC can work as all you need to know is whether the physical drive is being seen. If you try it from Windows, then you need to launch Disk Management (don't partition or format or you will lose everything) since Windows File Explorer won't see the drive.