A technical goal-scoring midfielder, Tvedten began her senior career with Avaldsnes IL, making her debut in 2016. She played a key role in the club’s historic Norwegian Cup victory in 2017, securing the first major trophy in their history.

After five years, she moved to Valerenga in 2021, where she established herself as one of the league’s standout performers. During her time in Oslo, Tvedten helped Valerenga to back‑to‑back league titles in 2023 and 2024, alongside Norwegian Cup victories in 2021, 2024 and 2025.

Known for her attacking output from midfield, Tvedten finished as Toppserien’s top scorer in both 2023 and 2025, netting an impressive 52 goals across four seasons with the club. Her consistency was recognised in 2024, when she was named Toppserien Player of the Year.