Dueling

In order to create a more interesting 1 vs 1 structured dueling system, here are a few (untested!) rules for dueling. In a structured duel, the participants have much more time to think, act, and have little to worry about outside interference. Thus, none of these rules are relevant in the fast pace of normal combat.
The rules follow as such:

Magic items, spells, healing potions, poison, and spectator interference are not allowed. Ranged weapons such as bows may be restricted, but a reasonable number of thrown weapons rarely are.
Waiting for the proper moment to strike is of the utmost importance, and lulls in a duel are common. Initiative is re-rolled every round. Conditions (prone, grappled, etc) incur disadvantage on initiative.
With little other than their opponent to worry about, their own positioning becomes key. Combatants that fighting from an elevated position have advantage on ranged attacks on those at a lower elevation, and enemies have disadvantage on melee attacks against those at an elevated position. (Provide interesting dueling arenas, and move around the battlefield to your advantage!)
There is only one person to focus on. Each combatant gains 1 Duel Action in addition to their usual action and bonus action. It can be used to Shove or Grapple, Attempt to Break a Grapple, Disengage, Add +3 to your next attack roll (offensive stance), or add +2 AC vs the next attack (defensive stance).

Magic items, spells, healing potions, poison, and spectator interference are not allowed.
Initiative is re-rolled every round.
Conditions (grappled, prone, paralyzed, etc) incur disadvantage on initiative
Combatants have advantage on ranged attacks made from an elevated position.
Combatants have disadvantage on melee attacks made against an elevated position.
Each combatant has 1 Duel Action in addition to their usual action + bonus action. It can be used to:

Attempt to Shove or Grapple (contested athletics v athletics/acrobatics)

Attempt to break a grapple.

Disengage.

Add +3 to your next attack roll (enter an Offensive Stance)

Add +2 to your AC against the next attack (enter a Defensive Stance)