The fighter is universal no matter what world she may be found. Most serve as gladiators, soldiers, merchant guards, or mercenaries. Most gladiators are slaves, but some can make a lucrative living as freemen, training a stable or earning prizes. The city-states rely on slave conscripts for the bulk of their forces, but all maintain a core of elite, trained soldiers such as the all-female Shadow Consorts of Nibenay or Urik’s Obsidian Guard. The merchant houses employ their own armies to protect trade, including well-trained cavalry and foot soldiers. Nobles keep their own bodyguards and small forces, considered a fairly easy job since most nobles are content to avoid conflict. Soldiers of fortune can be found in all settings, and a few have united to form small units operating from fortified bases, such as the Black Reavers outside of Urik.
Use the defaults from the Player's Handbook or Xanathar's unless changes are mentioned below. From any other book please check with the DM.
Eldritch Fighter, Arcane Archer, and Cavalier (Xanathar). Do not exist.
Rename Gladiator. While any fighter can take a weapon and enter the arena, there are a select few who have been trained to dominate and please the crowd. Outside the arena, this self-control translates well to command of soldiers.