The Arena Pit is in the northeast quarter of Dragonstar East, situated upon the main road through the city.
Tekin will point out you look like you have fighting skills and will ask you if you want to fight in the pit. He mentions that he thinks of himself as an entertainer and there is a gold purse reward for the winner. He then explains that the rules of the Arena Pit are simple, fights are to the death and there are no rules.
Melee opponent. Reward is 350 gold. After this fight, Tekin tells you that you have gained many fans and no-one wishes to challenge you, apart from Tekin's Champion.
Tekin takes great care to inform you that his champion is undefeated. As all fights are to the death you would assume that everyone fighting had also won all their prior matches.
In many ways this is a simpler version of the Arena Quest in Oblivion, although obviously much shorter.
This isn't a standard quest - it does not appear in the list of quests on your character sheet.
The XP value for the fourth opponent is clearly too low, but the value stated here is accurate.