Nissen was raised in Winmalee, The Blue Mountains, New South Wales, Australia to Danish-born parents. Her mother and father emigrated from Denmark to Australia when they were 11 and 22 years old, respectively. Nissen grew up on her parents' country property in the Lower Blue Mountains with her older sister. She attended Winmalee High School, where she obtained her HSC in 2013. Throughout high school Anja was part of the exclusive Talent Development Program and competed in a number of singing competitions. In 2008, Nissen made it to the semi-finals of Season 2 of popular talent-search TV show, Australia's Got Talent, aged 12. Since then she has appeared on a number of TV shows, including Young Talent Time, Mornings with Kerri-Anne and the annual Schools Spectacular. She also performed the Danish National Anthem in the company of Crown Princess Mary of Denmark.
2014–2016: ''The Voice Australia''
In 2014, Nissen was a contestant on the third series of The Voice Australia. She was a member of Team will.i.am, and went on to win the competition. Nissen's debut self-titled album consisted of songs from The Voice. It was not promoted by a radio single at the time, which impacted sales. Nissen later recorded a collaboration with will.i.am and Cody Wise titled "I'm So Excited", which received a mixed response. Soon after its release, Nissen began writing material in Los Angeles and Denmark for her eventual follow up EP. denotes winner. On 19 May 2015, Nissen released her follow-up single of Bacharach and David's "Anyone Who Had a Heart" as a part of Nine Network's hit television program Love Child. The song achieved over 70,000 views on YouTube. On 4 August 2015, Nissen released her third single "Triumph". She performed her single on The Voice Australia 2015 to over 1.6 million viewers nationwide. The song has over 15,000+ views online. Anja was also featured on We Love Disney album singing "A Dream is a Wish Your Heart Makes" from Cinderella. Her rendition of "Joy to the World" was released on The Salvation Army's Spirit of Christmas 2014 album.
On 10 January 2016, Nissen was confirmed to be taking part in the Dansk Melodi Grand Prix 2016, Denmark's national selection for the Eurovision Song Contest 2016, with the song "Never Alone". The song was written by Danish Eurovision winner Emmelie de Forest, producer Rune Westberg, and American singer and songwriterMoZella. She ended up placing second in the final with 36% of the final vote, behind winners Lighthouse X. The following year, she returned to the Dansk Melodi Grand Prix with the song "Where I Am", which was written by Nissen herself, along with Angel Tupai and Michael D'Arcy. Nissen went on to win, getting 64% of the final vote, and represented Denmark in the Eurovision Song Contest 2017. In May, Nissen released a 6-track EP titled Where I Am. Anja is currently living in Los Angeles, where she is studying Keyboard Technology and Music Theory.