Myhra progressed through Odd's youth academy but failed to make his breakthrough in the first team. On 1 January 2019, following the expiration of his contract with Odd, he signed with Strømsgodset.[2] He initially became the starting goalkeeper at the beginning of the 2019 season but lost his position in May 2019 when head coach Bjørn Petter Ingebretsen stepped down due to health reasons.[3] He reclaimed his position as the first-choice goalkeeper at the start of the 2020 season and was honoured as Player of the Season by the local newspaper Drammens Tidende at the season's conclusion.[4]
On 31 January 2024, Myhra signed a five-year contract with Danish Superliga club OB.[5] He immediately established himself as a starter in goal, but was unable to prevent OB from being relegated to the Danish 1st Division for the first time since 1998.[6][7]