Please note that this page and some of the pages for Companions and Unique Settlers with Leader Cards are currently under construction and thus incomplete.
All Vanilla Companions have Leader Cards and can be assigned as Mayor of one of your settlements.
Some of the Unique Settlers also have Leader Cards.
The effects that Leader Traits have on settlements are documented here: City Leader Traits.
Additional information can be found under the heading Assigning City Leaders on the Settlements & Cities page.