On June 25, 2016, Moverare was selected 112th overall by the Los Angeles Kings in the 2016 NHL Entry Draft.[2] He was soon signed to a three-year, entry-level contract with the Kings on July 15.[3] Signalling his intentions to continue his development in North America, Moverare was selected 20th overall in the 2016 CHL Import Draft by the Mississauga Steelheads of the Ontario Hockey League (OHL), agreeing to terms on August 9.[4]
Following two seasons of major junior ice hockey with the Steelheads, Moverare embarking on his first full professional season attended the Kings' 2018 training camp. On September 23, 2018, Moverare was cut from the roster and initially reassigned to join the training camp of American Hockey League (AHL) affiliate, the Ontario Reign.[5] With a surplus of defenceman within the Kings organization and with the interest of guaranteed icetime, Moverare was loaned by the Kings back to the SHL, to continue his development.[6] Opting to not return to HV71, Moverare secured a season long agreement with Frölunda HC for the 2018–19 season on September 24, 2018.[7]
On March 6, 2024, Moverare signed a two-year contract extension with the Kings.[8]