Shakespeare's Planet introduces the reader to a number of characters and species that could be the central part of future books by Clifford Simak. But as far as I know, they are not.
Ship: three human minds slowly evolving into a consciousness greater than the sum of the three.
Horton: a geologist by training, he knows he is 1000 years removed from the rest of humanity because of the cold-sleep while traveling.
Elayne: an explorer by nature, she is mapping the tunnels throughout the galaxy.
Carnivore: a species dedicated to being the supreme predator.
Nicodemus: a robotic AI with an apparent consciousness.
Pond: I'm still not sure what Pond is, but a single entity scattered throughout the galaxy.
Evil Thing: Not too powerful that Carnivore can't handle. With apologies to Ripley in Aliens, who laid the egg?
Dragon Thing: another strange species, encased in a cocoon of ... time?
Slugs: builders or maintainers of the galactic tunnels.
Shakespeare: with the influence of Pond, is Shakespeare really dead?
As a story, Shakespeare's Planet is uneven and feels unfinished. However, the focus of the story is on its strangeness. I can envision Iain M. Banks being inspired to write his Culture books after reading Shakespeare's Planet.
The issue of humans meeting again after a gap of 1000+ years is also explored in 3001 The Final Odyssey and Spin, among other books.