Easter Chile is one of the most off the beaten path island destinations in the world. Internet connectivity is a challenge here. Reliable internet on the island is only found on the island's main town of Hanga Roa. Outside Hanga Roa get ready to be disconnected.
Best sim card to use on Easter island: Entel and Movistar. Don't order sim cards online while you're in Chile, they'll ask you to provide a RUT number ( a Chilean tax number ) which you can't have if you're a tourist. You can buy sim cards in Santiago airport or in Hanga Roa Entel shop. They won't ask you for a RUT number if you purchase the sim card personally at shops since they know you are a tourist.
Most hotels and cabins have WiFi, though where I was staying wi-Fi is only strong enough in common areas. Internet connectivity inside most rooms was poor.
Hotel wifi barely supports streaming or video calls. If you need a stable internet the place to find it is at cyber cafes in Hanga Roa. There are about 4 cybercafes along Hanga Roa's main street Atanu Tekena. Omotohi cyber cafe, the oldest on the street also has another branch just near the Santa Cruz church.