I wouldn't recommend this to someone who has never read PD James before. It isn't the strongest of her books in several respects. Additionally, James seems to be working purposefully with unease, missed connections, unclear futures and lack of meaning. I tend to think that someone who trusts and is familiar with her work will give her the slack to try those elements out as part of the mystery novel. However, they aren't the kinds of plot points that make for a satisfying novel, full of closure.
What do I mean by this? For example: Clues that feel significant, and that lead nowhere. Note that I don't mean red herrings-- I mean clues that literally lead nowhere. There are red herrings too, but there are also unexplored moments of the kind that normally mean something in detective books. Also, I think that there's something odd about the way that she handles Rhoda as a character. James puts us into her perspective and lets us have access to her as a living character for nearly 125 pages. Not bad by itself, but after that, Rhoda is left a cipher. Her death feels utterly disconnected from what we know of her life. It creates a jarring effect (and results in many of the thrown away clues that I mentioned earlier). She has her secrets as well. We're given glimpses of them, but they remain tantalizingly opaque.
There are also the issues with AD and his special investigations squad-- the looming dissolution of the unit hangs over the book. It feels as though James has as much desire to tie up the loose ends in her character's lives as much or even more than she wants the murder to be solved. Actually, the solution to the murder is neither simple nor clear-- I was left feeling frustrated myself and not quite smart enough to get what either James or AD were driving at. But it isn't, somehow, the main point of the novel either.
PD James has a lot of credit with me, and I enjoy her writing very much. That remains true in The Private Patient. Even a flawed James is better than much of what is out there on the market-- at least for this reader. This said, The Private Patient is an odd sideways kind of book, and its concerns are not typical for a mystery novel. If you want a typical mystery novel, look elsewhere. (And sometimes you really don't want to have to work to read a book.) If you want a typical James/Dalgliesh novel, look into her earlier work.