Unavoidably (at least for me), when I started planning a course called "Studies in the Novel: Mystery and Detective Fiction," I gravitated toward the Shakespearean possibilities. Ngaio Marsh will make an appearance with her Death at the Dolphin (for which, q.v.), though not with her Light Thickens (for which, q.v.). Agatha Christie's Nemesis (for which, q.v.) may be assigned to a group—but for reasons besides its use of Shakespeare.
But I've also been exploring novels that have some sort of Shakespearean connection that I'd not previously read.
Ellery Queen (under the pseudonym Barnaby Ross) has written four Drury Lane novels; this, as may be evident by the title, is the final one.
I came to Drury Lane's Last Case without encountering the hearing-impaired, lip-reading, former-Shakespearean-acting amateur detective in the other novels (The Tragedy of X, The Tragedy of Y, and The Tragedy of Z for those of you keeping score), and I think having done so would have increased my enjoyment of this one—but it also worked very well as a standalone mystery.
During Shakespeare's lifetime, a volume of poetry entitled The Passionate Pilgrim was published under Shakespeare's name—though only about 25% of the poems were authentically by Shakespeare. Its first edition was printed in 1599 (or, possibly 1598); a second, expanded edition was printed in 1612.
As Grandmother Jones used to say, I told you that to tell you this. Part of the plot of Drury Lane's Last Case involves the theft of the rare 1599 edition of The Passionate Pilgrim . . . and its immediate replacement with the even rarer (in the world of the novel; elsewhere, it's non-existent) 1606 edition!
All that is part of a larger mystery, but that's the primary Shakespearean connection.
Here's a representative chapter (apologies for the difficulty of reading the later pages, but I didn't want to damage the binding of the 1946 edition I had in hand):
