It was written by one of the four (or five) "Lions" of post-war Dutch literature. The story concerns an old retired actor who lives alone. He has had some mysterious dealings with his older (or younger) family members. One day he receives an anonymous letter in the post offering him one last role in a Shakespeare revival (King Lear, Hamlet, The Tempest?). He decides against it then changes his mind...
The novel's main character is Willem (Uli) Bouwmeester, a retired actor who used to work mainly in night clubs and revues. He receives an offer for the lead role in "Noodweer" (literally "Tempest"), a play about the stage actor Pierre de Vries. Uli accepts the offer but the strain of the preparations and rehearsals causes a stroke. He dies and is "reborn" as Pierre de Vries; as Pierre de Vries he plays the lead role in the première of Shakespeare's The Tempest at the Stadsschouwburg of Amsterdam at the end of the nineteenth century. (In other words, Uli travels back in time / becomes Pierre de Vries.)
In the sources I found on the web, i.e. this Dutch Wikipedia article and this review by a secondary-school pupil, there is no mention of an anonymous letter or of mysterious dealings with other family members. (Uli comes from a family of actors but had only a second-rate career in comparison with the others.)