When it isn’t being cut, they have submarine cables to Norway.

https://en.wikipedia.org/wiki/Svalbard_Undersea_Cable_System

The Svalbard Undersea Cable System is a twin submarine communications cable which connects Svalbard to the mainland of Norway. The two optical fiber cable consist of two segments, from Harstad to Breivika in Andøy, and from Breivika to Hotellneset near Longyearbyen in Svalbard. The segments from Harstad to Breivika are 74 and 61 kilometers (46 and 38 mi) long, respectively, and the segments from Breivika to Hotellneset 1,375 and 1,339 kilometers (854 and 832 mi). Each consists of eight fiber pairs and there are twenty optical communications repeaters on each segment. Each segment has a speed of 10 gigabits per second (Gb/s), with a future potential capacity of 2,500 Gbit/s. The system is now the sole telecommunications link to the archipelago.

There’s apparently 5G service:

https://www.lifeinnorway.net/5g-norway/

The company began Scandinavia’s first 5G pilot back in November 2018, conducted Norway’s first 5G video call, and launched the world’s northernmost 5G pilot in Svalbard. Telenor chose Nordic company Ericsson over Chinese firm Huawei to supply the critical infrastructure for the rollout.

I don’t know whether Starlink orbital paths can cover that far north.

googles

Apparently so, and they started service about five months ago.

https://satprnews.com/2023/07/09/starlink-launches-in-svalbard-a-new-era-of-internet-connectivity-in-the-arctic/

Starlink Launches in Svalbard: A New Era of Internet Connectivity in the Arctic.