Greer was a regular contributor to BBC Two's Newsnight Review, and has been a panelist on the BBC's Question Time programme. She appeared on the edition in October 2009 that also featured Nick Griffin, then leader of the British National Party. Commenting after the recording she called it "probably the weirdest and most creepy experience of my life". The encounter formed the basis for her opera, Yes, written for the Royal Opera House with music by Errollyn Wallen, and which premiered there at the Linbury Studio Theatre in November 2011. She was formerly director of the Talawa Theatre Company and has served on the boards of the Royal Opera House and the London Film School. She is also a former theatre critic for Time Out magazine.
Greer's book Obama Music, partly a musical memoir, was published by Legend Press in October 2009. Reviewing it in The Independent, Lesley McDowell said: "Greer expertly weaves in memories of her own upbringing in Chicago, with more humour than you might expect, along with a clear, defined passion for the music she grew up listening to. She wants to show, too, how both the place she lived in, and the songs she listened to, were full of unseen boundaries that had held people back – but also gave them something to fight against." Her biography of Langston Hughes, Langston Hughes: The Value of Contradiction, was published in 2011 (Arcadia/BlackAmber Inspirations). Greer co-produced a documentary film, Reflecting Skin (directed by Mike Dibb) – on representations of black people in Western art – which was shown by the BBC in 2004. She is currently working on a novel about Rossetti. Greer's memoir A Parallel Life was published in 2014 and was described by Joy Lodico in The Independent as "the story of a journey deliberately and bravely taken against all expectations".