HQ published Frank's debut, The Lost Ones, in 2018, followed by The Return last year.
Mills said: "Anita is an incredibly skilful historical novelist and having breathed life into the ghost story in her debut, The Return shows Anita is a hugely versatile and brilliant novelist. This glorious, beautifully drawn love story tells the story of Jack, who, on the eve of the Second World War, promises his wife he won't return home when the war is over. Readers have been absolutely falling in love with it. Anita has so many ideas and stories she wants to tell, I can't wait to see what she writes next. Everyone at HQ is very much looking forward to continuing to work with her."
Headley said: "On the strength of Anita's beautiful novel, The Return, I am delighted that Kate and HQ have invested in two more books. Anita is such a gifted writer and I am delighted readers can look forward to reading more from this extraordinary storyteller."
Frank said: "I feel incredibly lucky to be able to carry on working with Kate and the brilliant team at HQ. I am very grateful not only for the support that Kate and David have extended to me over the last couple of years, but also for their unwavering faith in my writing, and thanks to them both, I now find myself in the perfect position to share more of my stories. I am very happy indeed!"