She began her acting career at the Huon Valley Theatre Company, before attending the National Institute of Dramatic Art.
In 2010, Sveen starred in the multi-story drama film Before the Rain and made a guest appearance in the soap opera Home and Away.
The following year, she announced her departure from Home and Away, after she was cast in the Seven Network drama The Secret Daughter, alongside Jessica Mauboy.
Her acceptance speech was praised by the media and viewers after she spoke about positive body images and acknowledged Indigenous Australians as the original owners of the land where the Logies were held.
[17] In early April 2016, it was announced Sveen had joined the cast of The Secret Daughter alongside singer Jessica Mauboy, who encouraged producers to sign her for the show.
She posted a goodbye message on her social media account, stating "If someone had told me 10 years ago that I'd be playing a staunch, surfie chick in Summer Bay (and that it would bring me more joy than I could imagine) I wouldn't have believed them.
"[19] Sveen appeared in Storm Ashwood's war drama film Escape and Evasion as journalist Rebecca in 2019.
[21] In October 2023, Sveen began filming a role in romantic comedy feature He Loves Me Not, alongside her fellow Home and Away co-stars Rhiannon Fish and Georgie Parker.