Indeed, DC Comics did quite a few sequels to
TOS episodes in their time. As well as the examples that Christopher noted, there was a two-parter which was a sequel to "Wolf in the Fold", a sequel to "Tomorrow is Yesterday" and a three-issue story which returned to the planet from "The Apple", a sequel to "The Tholian Web" in "Raise the Defiant!" and many more.
I know they might not be what you're looking for, but there was "The Peacekeeper" 2-parter which featured Gary Seven and Isis and introduced the Aegis, the return(s) of Harry Mudd as well as other characters such as Robert Fox, Finnegan, you name it.
On the novel front, I think there have been fewer prequels and sequels.
Yesterday's Son and
Time for Yesterday are sequels to "All Our Yesterdays",
Double, Double is a sequel to "What Are Little Girls Made Of?",
The Cry of the Onlies is a sequel to "Miri" and "Requiem for Methuselah",
Firestorm is a sequel to "Elaan of Troyius",
Assignment: Eternity is a sequel to "Assignment: Earth" and a prequel to
Star Trek VI: The Undiscovered Country,
The Eugenics Wars were a prequel to "Space Seed" and
Star Trek II: The Wrath of Khan,
One Small Step was a sequel to "That Which Survives",
Garth of Izar was a sequel to "Whom Gods Destroy".
A bit of a list and some more direct than another. And this is only
The Original Series!
