Skellern attended the University of Sydney, where she was a prominent student Activist. In the first season of The Chaser's CNNNN, an Australian television show satirising American news channels CNN and Fox News, she played her namesake Anna Skellern, a no-nonsense war correspondent noted for the frequent loss of her cameramen and dubbed 'the perfumed abattoir'. In 2004, CNNNN shared the Logie Award for 'Most Outstanding Comedy' with Kath & Kim.
In 2007, Skellern was at the centre of a public spat between two of her former boyfriends, singer-songwriter Tim Freedman and Comedian Chris Taylor. On 7 October 2007, Freedman posted a message on the band's official website, citing a parody of him which was written by Taylor, and had aired on the 3 October 2007 episode of The Chaser's War on Everything. The song was performed by fellow Chaser Andrew Hansen, and the lyrics implied that Freedman was obsessed with the Sydney suburb of Newtown, and that he continually referred to the area of Newtown in his own songs. In his message, Freedman alluded that the lyrics were indeed written by Taylor, and that the parody had been motivated by jealousy over Skellern.
In 2009, Skellern filmed Agatha Christie's Poirot: The Clocks with David Suchet, Jamie Winstone and Tom Burke. She also filmed the new role of restaurant worker, babysitter, and Jake's crush, Kelly, for BBC1's award-winning, partly improvised comedy Outnumbered, directed by Andy Hamilton and Guy Jenkin and starring Claire Skinner and Hugh Dennis.
She played the role of Lexy Price in series 2 of Lip Service broadcast on BBC Three in April 2012. In October 2012 Skellern played Elaine White in series 2 episode 2 of the Sky 1 comedy drama series Spy.
Skellern was cast as the new Sapphire in the radio show Sapphire and Steel from Big Finish – beginning with "Second Sight".
