Reckoner's Arena

If I hold Reckoner's Arena with Yone, Blademaster, will I place his triggered ability on the chain when the hold effect of Reckoner's Arena resolves?

No, you will not. The main thing you need to know is that activating a conquer effect such as the Reckoner's Arena effect is the equivalent of checking the condition of all of the specified conquer effects, as if a conquer had occurred at Reckoner's Arena. Any triggered abilities of units at Reckoner's Arena that trigger on conquering will see a conquer event occurring, but they will still need to check their other conditions in order to go on the chain.

In this case, the rest of Yone's conquer effect condition is "...that was previously uncontrolled," and since the battlefield wasn't previously uncontrolled, Yone's ability will not trigger.

Note that no actual conquer occurs-we're simply treating the game as if a conquer had occurred at that battlefield for the purposes of the specified abilities. In Reckoner's Arena's case it specifies units, so only units with conquer effects at Reckoner's Arena will see this conquer event and potentially trigger.

(We recognize the rules for "activate" in the way discussed above are underdefined. Expect further revisions in the next rules update.)

383.4.g.1. To do so, that player checks the condition of all of the specified effects, as if they had fulfilled the named part of the condition. Example: Reckoner's Arena reads "When you hold here, activate the conquer effects of units here." For each unit at the battlefield, you will check the trigger condition of their conquer effects to see if the condition has been fulfilled, treating the conquer portion of the condition as having been fulfilled. If all of the conditions are fulfilled for a conquer effect, it is placed on the chain as if it had just triggered. If any of the non-conquer parts of the condition are not fulfilled, it will not be placed on the chain. Example: A spell reads "Activate the play effects of your gear." For each gear you control, you will treat it as if you had just played the gear and check the other conditions of that gear. If all of the conditions are fulfilled for a play effect, it is placed on the chain as if it had just triggered.