As of now, there is no permission that can be applied to user(s) / group(s) on which tab can be displayed for the particular screen since users who are able to make use of the screen will be able to see all the tabs:

As an example, you can see the following in the Create Issue screen:

As an example, there are different departments that will access this screen with different permission. Department A only has the permission to view Tab 1 (Tab 2, Tab 3, and Tab 4 are not visible).

On top of that, the tab can also be dynamic in a sense that when a default system field / custom field has a certain value, Tab 3 will be enabled (for an example).