Drayton graduated from the Arts Educational School in Chiswick (London, England). In 2013 Drayton performed in the 2013 Downton Abbey Christmas special, as the character Madeleine Allsopp alongside Paul Giamatti. The following year Drayton was cast as Amberle Elessedil, one of the lead roles in the MTV fantasy drama series The Shannara Chronicles; the series premiered on 5 January 2016. Drayton has also done stage work, appearing in The Green Bay Tree at the Jermyn Street Theatre in London in 2014 and as Juliet in Romeo and Juliet at the Stafford Shakespeare Festival in 2012.