You can fight a duel with Aidan Sitabo while in Cliff's Edge. This activity is not considered a separate quest and is not marked in the journal in any way. You won't unlock any additional mission this way, either. It is but an extra activity that you can do while exploring the city. It's worth it to fight the duel due to the possibility of permanently increasing one of the Stats. It's a good idea to rest in a tavern beforehand, though, since you will have to pass several quite difficult checks and therefore additional points will be very useful.
To start the duel, find the person standing by the fountain in the main square. The man is named Aidan Sitabo (M6.1). Interact with him and click through the conversation until you find the "I bet I'm faster than you" option. Now you have to pass several checks. The first one requires Speed and the Quick Fingers skill. If you fail it, you receive minor damage and you won't be able to repeat it.
After the first test, choose the "I'm ready for another part of your test". The second test also makes a Quick Fingers check. If you don't manage to pass, you receive damage to Might points pool but you can reattempt to pass the test.
If you pass the second test, choose the "So? Did I pass all your tests?" option. Confirm your willingness to start the last test which is a fight to the death. In this case, you can use Speed and Quick Fingers or Might and Smashing. Completing the last test gives you 2 XP and 1 permanent bonus point to your character's Speed. This isn't everything, though, since you can decide Aidan's fate afterwards. If you choose to snap his neck, then your Speed is increased by 1 point again (which in total gives you 2 points!).
If you fail the last test, your character dies. However, don't worry since you'll respawn in the sanctuary from the prologue. Go through the portal and you will appear in Dendra O'Hur Chapel in Underbelly. Exit the building and visit Aidan Sitabo again. Interact with him and choose the first dialogue option to propose a rematch. The opponent will refuse but you will be given a reward: a cypher called Dynamic Hourglass.