I remember there being a panel with buttons to zoom in or out or pan in the viewport but it seems to have gone somehow. How can I add it back?
The tabs on the toolbar come from addons, if one is missing then the addon that put it there has been disabled or uninstalled.
The steps you list are available using the mouse and keyboard, use ⇧ Shift MMB to pan, the scroll wheel as well as ⎈ Ctrl MMB will zoom in/out.
Like the others who have answered/commented, I can't remember ever seeing a panel with navigation tools in the current or past versions of Blender.
Are / were you using the (unstable) Blender 2.8 Alpha?
One possibility I can think of is that you've been using the recent (unstable) version 2.8 Alpha, and then reverted back to the (stable) version 2.79.
This is what the "gizmo tool" looks like in Blender 2.8 Alpha:
If that's what you were using, and now for some reason you are using Blender 2.79, then you can find the releases here to install Blender 2.8 back. Be aware that 2.8 Alpha is still unstable and you must be very careful about using it for important projects.
If that's what you were using, and you are still using 2.8, then you might have hidden the Gizmo. You can bring it back by reactivating (if needed) the Overlays and, in the Overlays menu, activating Gizmo: