Hope studied French and Spanish at the University of Oxford. While there, she found an agent and began acting professionally. She later enrolled at the Le Coq Theatre School to Paris to study drama and acting.
At the University of Oxford, she found an agent and began acting professionally. Her first role in a film was as a Factory Woman in the 2012 musical Les Miserables.
In 2013, Hope began playing the role of Ramsay Bolton's sadistic lover, Myranda, in HBO's fantasy drama series Game of Thrones. She continued in the role until the character died during the fifth season and her body found in the sixth season premiere.
In 2014, she guest-starred in the second season of The Musketeers, playing the role of Charlotte Mellendorf.
That same year, she appeared in the film The Theory of Everything, portraying Philippa Hawking, the younger sister of Stephen Hawking. In 2015, she had a leading role in the British gangster film North v South as Willow Clarke. That same year, Hope appeared in the music video "Beautiful to Me" by Olly Murs.
In 2016, Hope appeared in the biographical romantic drama A United Kingdom, and the romantic thriller Allied. In 2017, she had a supporting role in the drama film Three Christs and in 2018, she co-starred in the horror film The Nun.
Hope has also done theatre work, including Broadway shows such as Buried Child where she played the role of Shelly in 2016. In 2017 she played the role of Zara in Almeida Theatre's Albion and in 2018 she played as Dr. Michaels' mother in The New Group's Good for Otto.
In 2018, she was cast as Catherine of Aragon in the new Starz / New Pictures series The Spanish Princess (2019), a follow-on from cult hits, The White Princess (2017) and The White Queen (2013).
In January 2020 she appeared as Annabel Connors, a main character in Season 2 of Bancroft opposite Sarah Parish.
In March 2018, Hope was cast in the lead role of the Starz series The Spanish Princess, in which she plays Catherine of Aragon. The show is a follow up to The White Queen and The White Princess.