Cortana's actor for the Halo TV series was recast due to scheduling conflicts, and it has the best possible replacement lined up: Cortana's actor from the video games.
The role of Cortana will now be played by Jen Taylor, the actor who brought Cortana's voice to life throughout the Halo series and as Microsoft's digital assistant, as reported by IGN. Showtime isn't yet ready to confirm whether Taylor will physically appear in the show, or if she'll be voicing a computer-rendered character. Cortana is a fully digital entity herself, so it wouldn't be surprising if Showtime opts for the latter option.
The Truman Show's Natascha McElhone was originally set to play the role of Cortana, but scheduling conflicts brought on by the pandemic mean she's no longer available for the role. McElhone will still portray Dr. Catherine Halsey, who oversaw the Master Chief's supersoldier program and was Cortana's original creator.
In the games, Taylor provides the voice for both Cortana and Halsey, since Cortana is a sort of digital clone of her creator. We don't know if or how the Showtime series will address this difference from the video game fiction, though admittedly it could be as simple as saying "she decided to make Cortana sound like somebody else instead."
The Halo TV series resumed filming today, marking the occasion with our first look at Master Chief actor Pablo Schreiber partially in costume. It's just the lower half of his helmet, but it is still cool to see.