There is no one-click duplicate button for lists. The supported paths depend on whether you want to copy a static list (fixed membership) or re-use the filters from an existing saved search (dynamic list).
Copy a static list by opening it and saving under a new name
Open the list you want to copy from the Lists page.
Apply any additional filters you want, or leave the current view as-is.
Click Save As in the toolbar.
In the "Save As" modal, type a new name in the Name field.
Choose List as the save type. This captures the current contacts as a static list that will not change over time.
Set Visibility (Everyone, Only me, or Specific people).
Click Save. You are taken to the new list.
The original list is unchanged.
Re-use the filters from an existing saved search
If your list was saved as a saved search (dynamic), you can reload its filters and save them as a new list:
On the Lists page, find the list whose filters you want to copy.
Click the actions menu (the three-dot icon) on that list row.
Click Load Filters to Create a List. This navigates to the People page with the original filters pre-loaded.
Adjust the filters if needed.
Click Save As, give the new list a name, choose List or Saved search, and click Save.
Sharing an existing list instead of duplicating it
If the goal is to let another person use the same list rather than creating a separate copy, you can change who can see the list without duplicating it:
On the Lists page, click the actions menu on the list row and choose Edit Details.
Change Visibility to Everyone (visible to all org members) or Specific people (lets you pick individual users).
Click Save.