Does a clone that copies a legendary creature cause the legend rule to apply?

When a Clone or any copy effect enters the battlefield, it copies the copiable values of the chosen permanent, which includes all characteristics printed on that card — name, mana cost, type line (including supertypes like Legendary), subtypes, rules text, and so on (CR 707.2). The Clone itself becomes legendary.

The legend rule (CR 704.5j) states that if two or more permanents with the same name are legendary and controlled by the same player, that player chooses one to keep and puts the rest into the graveyard as a state-based action. This rule checks supertype and name simultaneously.

So if you control a Sigarda, Host of Herons and you play a Clone copying it, you now control two legendary permanents named Sigarda, Host of Herons. State-based actions immediately apply and you must put one into the graveyard — you choose which one to keep.

Importantly, this is true even if your opponent controls the original. The legend rule only applies among permanents controlled by the same player. If your opponent controls Sigarda and you Clone it, both players each control one Sigarda — no legend rule triggers for either player.

One nuance: if you Clone a legendary creature your opponent controls and you have no other copy of that legend, you simply control a single legendary permanent and no legend rule applies at all.