In a television landscape riddled with reboots, sequels and revivals, audiences are primed for stories that pick up where another tale has left off. Figuring out how to continue the narrative of a longtime franchise or beloved character isn’t always easy, but when done well, can translate to loyal fans — and even Emmy attention, as in the case of AMC’s “Breaking Bad” prequel, “Better Call Saul.” This season, several TV series are keeping well-known lore alive, but evolving their stories in new and sometimes unexpected ways.

Among the shows that are continuing journeys of known characters are everything from “Power Book II: Ghost” at Starz, to NBC’s “Law & Order: Organized Crime,” the latter of which has revived beloved detective Elliot Stabler, played by Christopher Meloni. Other series pick up characters or universes in slightly less conventional ways.

In Treatment,” for instance, returned for a fourth season on HBO on May 23, more than a decade after ending a 106-episode run. Uzo Aduba has succeeded Gabriel Byrne as the show’s therapist, playing his protégé, Dr. Brooke Taylor, complete with her own wave machine from the Institute.

“We were always cognizant that we had to honor the first three seasons, while trying to do our own thing,” says “In Treament” co-showrunner Joshua Allen. He and co-showrunner Jennifer Schuur wanted the new edition’s therapist to be a Black woman, and sought to make her roster of patients more diverse as well.

“We wanted to build that connection, so that people who love the first three seasons weren’t going to be like, ‘Oh, this is just some brand new thing that they’re calling “In Treatment.”’ We also wanted to make sure that we left room for people who hadn’t seen the first three seasons to just jump in with us, and they’d be able to ride the ride,” says Allen.

There are certain advantages to continuing known IP, says Schuur, but the challenge was figuring out how to make Season 4 feel like part of the “In Treatment” universe. The pandemic prompted the team to make some technological updates, with Anthony Ramos’ Eladio becoming a Zoom patient.

“COVID is absolutely a factor in the show,” says Schuur. “It is part of the reality that these characters are living in, but it’s not the focus of the show. Instead, it’s about the inner lives of these very particular characters who represent a wider range of perspectives than I think we’ve seen before from ‘In Treatment.’”

The show even brought back a number of producers from the original “In Treatment,” which drew a real “institutional wisdom” into the new season, says Allen, who sought to maintain the intimacy but update certain elements, such as exploring the central therapist’s own mental health struggles.

Picking up a new season of a long-ended show — instead of straightforward reboot — may seem unusual, but it’s not the only new drama in the 2020-21 TV season that is threading stories from years ago.

CBS’ “Clarice” is run by Elizabeth Klaviter alongside executive producers Alex Kurtzman and Jenny Lumet. Klaviter says this continuation comes from “a place of deep love and respect for Thomas Harris and the universe he created.”

Rebecca Breeds assumed the mantle of the eponymous character, Clarice Starling, and events in the series follow on those from the 1991 film “Silence of the Lambs,” itself an adaptation of one of Harris’ novels.

Reviving an iconic character while breathing new life into it is a tricky balance. But, “from her first audition, [Breeds] brought to the role echoes of Jodie Foster’s role,” Klaviter says. “You definitely see the relationship between the two performances, and yet she managed to make Clarice completely her own, and expand the character to a television-sized character where we’re investigating myriad of nuance of who this woman is. I just think she’s done an incredible job, both bringing the vulnerability and the strength [to] the iconic Clarice that we all know and love from ‘Silence of the Lambs.’”

Set a year after Buffalo Bill and the events of “Lambs,” “Clarice” focuses solely on her and not Hannibal Lecter. (MGM holds the rights to “Lambs” so his name is not legally allowed to be uttered on the CBS series.) That has given Klaviter and co. room to connect Clarice to a modern audience.

“I feel like as an ambitious woman in your 20s, you come out of the institutions that have raised you,” says Klaviter. “In Clarice’s instance, she went to college and then studied psychiatry and then went on to Quantico. And now she is on her own in the world for the first time, trying to figure out who she is as a human, while she’s figuring out who she is as an FBI agent. That’s the intersection of the freedom that you get as you enter your early adulthood, where you also have to figure out how to integrate the baggage that you carry with you. So seeing her sort through her PTSD — not just that she experienced from Buffalo Bill’s basement, but also from our childhood and having to sort it out — I think is something that women can relate to.”

“Clarice” is not the first TV adaptation of Harris’ work. Many will recall that NBC’s “Hannibal,” which ran from 2013 to 2015, was generally well-received by critics and earned a loyal fanbase. Ultimately, the series faced low viewership woes, serving as a reminder that even the most high-profile of continuations are vulnerable.

But that isn’t something these new showrunners are worrying about.

“I really tried to put the pressure aside and really embrace my love for the property, and invest all of my passion and all of my love of the characters and of storytelling and the tone and the universe and try to take that to the screen,” Klaviter says.