this sounds like a crossover thread.
ill give some UK examples
TheBill & MIT epsidoe 1, on the Bill one of the cast was killed, and in the first episode of MIT, the MIT cast investigated who killed him.
Holby City & Holby Blue, in an episode of Holby City a doctor was attacked and it looked like she killed her attacker, in the first episode of Holby Blue S2, the Holby Blue cast investigated the crime.
there is a Sarah Jane Adventures episode " The Last Sontaran" that follows on from the evens of the Doctor Who episode The Sontaran Stratagem/Poison Sky.
Same goes for Torchwood episode Cyberwoman, that follows up the events of Doomsday.
I used to have a list of UK crossovers & spin-offs but I lost it
The Voyager episode "False Profits" is a sequel to the TNG episode, The Price