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.
Relocating to London, in July 2007 Skellern graduated from the Guildhall School of Music and Drama. That same month she made her professional stage debut in the successful West End production The Vegemite Tales, playing the role of Maddie.
Skellern was cast as the new Sapphire in the radio show Sapphire and Steel from Big Finish – beginning with "Second Sight".
Skellern filmed for the sequel to Neil Marshall's critically acclaimed horror film The Descent, The Descent Part 2, which was released in late 2009. The script sees a survivor from The Descent forced back into the system of caves she battled her way out of in the first film, in a bid to locate the rest of her group. Skellern played one of the members of the new search team that accompanies the survivor back into the caves.
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.
In 2010, Skellern spent time in Africa filming the lead role in the thriller, Siren, with Eoin Macken and Tereza Srbova. She also plays Jo in the British miniseries, A Passionate Woman, directed by Kay Mellor and Antonia Bird, with Billie Piper and Sue Johnston.
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.
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.
Taylor denied this, and said that the song had nothing to do with Skellern. "He [Freedman] was speculating that the song was written out of some sort of jealous rage or payback which isn't the case at all," he said. "My relationship with Anna didn't end badly... we're still good friends and see each other quite a bit."