Does clone copying a legendary creature immediately die to the legend rule if the original is still in play?

When Clone enters the battlefield as a copy of a legendary creature, it becomes a legendary permanent with the exact same name as the original. The 'legend rule' (CR 704.5j) is a state-based action that checks whether a player controls two or more legendary permanents with the same name. If so, that player chooses one to keep and puts the rest into the graveyard.

State-based actions are checked immediately after any game event, including a permanent entering the battlefield (CR 704.3). So the moment Clone resolves and enters as a copy of the legendary creature, state-based actions are checked and the legend rule triggers. The controller of the Clone must choose: keep the Clone or keep the original. The one not chosen is put into the graveyard (CR 704.5j).

Importantly, it is the controller of each legendary permanent who makes the choice — if your opponent controls the original and you control the Clone, each of you controls only one copy, so the legend rule does NOT apply. The legend rule only fires when a single player controls two or more legends with the same name (CR 704.5j).

Concrete example: You control Arcades, the Strategist. You cast Clone and have it enter as a copy of Arcades. You now control two legendary permanents named 'Arcades, the Strategist.' State-based actions are checked: you must choose one to keep and put the other into the graveyard. You could keep the Clone (since it entered with summoning sickness anyway) or the original — your choice.

One useful trick: Clone entering briefly still triggers any 'enters the battlefield' abilities before it is sacrificed to the legend rule, since state-based actions are only checked after the trigger is placed on the stack — but the legend rule itself is applied before any player gets priority (CR 704.3).