Drayton graduated from the Arts Educational School in Chiswick (London, England).
In 2013 Drayton was cast in her first major role in the Hallmark Channel television movie pilot for When Calls the Heart, in which she played Elizabeth Thatcher (a role that was taken over by Erin Krakow in the subsequent television series). This was followed by a role in the 2013 Downton Abbey Christmas special.
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.