This is an excellent mystery, first published in 1937, which was the heart of Agatha Christie's prime. Hercule Poirot receives a letter from an elderly woman who is seeking to hire him, but it turns out the woman had passed away several weeks before. Was her death from natural causes or was it murder? Not hard to guess the answer to that one! I found the mystery sufficiently baffling and the resolution satisfying.
Captain Hastings also appears in this novel, playing -- as always -- Watson to Poirot's Holmes. I've never quite figured out whether there is a way of accounting for Hastings's appearances -- he's there in most of the short stories, but in relatively few of the novels. At one point, if I'm remembering correctly, he shares a flat with Poirot, although not in this novel. Hastings is presumably living off a private income with plenty of time on his hands because he is always available to travel with Poirot in unraveling the mystery. Where he lives and what he does when he is not with Poirot is not discussed. In fact, the details of Poirot's life when he is not detecting are left unmentioned in this novel, and barely discussed in any of the others. Clearly, it wasn't Christie's style to get into what she surely must have considered nonessential issues.
While I would not put this among the very best of Christie's books -- The Murder of Roger Ackroyd, The A.B.C. Murders, or And Then There Were None would rank above it, in my view -- it is still very good and I would highly recommend it. Finally, you should note that this book was originally published under the title "Poirot Loses a Client."