By Merissa Marr 

Reminiscing about his soon-to-be ex-colleague Stephen Colbert on Thursday night, Comedy Central's Jon Stewart showed a classic clip of a young Colbert back in the days when he was a correspondent on Mr. Stewart's "The Daily Show."

"There's an allegation the prince had a gay experience?" Mr. Stewart asks a supposedly London-based Mr. Colbert in the clip. "Not gay Jon, aristocratic. It is a different culture than ours," responds Mr. Colbert as he provocatively peels a banana and puts the whole thing in his mouth.

While Mr. Stewart doubled up over his desk in laughter over the clip, it likely represented a bittersweet moment for the 51-year-old comedian. That afternoon Mr. Colbert, 49, had been named to succeed David Letterman as host of "Late Show" on CBS . A decade ago, it was Mr. Stewart being courted to host the "Late Show."

But for top executives at Comedy Central and its owner, Viacom Inc., it may be a more bitter than sweet moment. Since it first hit screens nine years ago as a spinoff from "The Daily Show," "The Colbert Report" has helped define Comedy Central's brand and has become a key part of the channel's schedule. Comedy Central is now scrambling to figure out a replacement.

"These are enormous shoes to fill," said Comedy Central's President Michele Ganeless. "But if this had to happen, it's a perfect time in our history to find the next great thing. We have the right roster of talent and creative."

On Thursday, as CBS went public with its new recruit, Comedy Central's top brass got right down to business, meeting its development team to brainstorm ideas on a successor to Mr. Colbert.

"The only limit is your imagination," Ms. Ganeless told the room of creative executives, who immediately started kicking around possible candidates within the Comedy Central family as well as talent outside the empire.

It could be Mr. Stewart who once again ponies up the next big thing. Over the past decade or so, his show has proved a farm team for all of Hollywood, generating such film and television stars as Steve Carell, Ed Helms and John Oliver, who is launching his own talk show on HBO later this month. Samantha Bee and her spouse, Jason Jones, are two current correspondents who are often mentioned as being ready for something bigger.

More broadly at the channel, there is Amy Schumer, who is making waves with her comedy, "Inside Amy Schumer." Television executives also mention Chris Hardwick, who hosts "@midnight," a new late-night show that follows Mr. Colbert's, and the two stars of the sketch comedy, "Key & Peele."

One person familiar with the situation said agents also started calling on Thursday, offering up a list of external candidates. It was a particularly busy day for agents, as speculation also swirled about the future of CBS's other late-night host, Craig Ferguson, who is in negotiations over a new contract for the 12.35 a.m. slot.

The new Comedy Central host will need to appeal to the 18-34 audience that the channel targets. While late-night trends slightly older, the channel's average viewer is around 30 and male--a contrast to broadcast television, where the average viewer is decades older and skews more to women.

Another job requirement: someone who complements Mr. Stewart but is also an up-and-comer who could rise to his level--as Mr. Colbert did. While Mr. Stewart draws a bigger audience, Mr. Colbert has been snapping at his heels both in terms of viewers and advertising revenue.

Mr. Stewart has hosted "The Daily Show" for the past 15 years and his own contract expires in September 2015. While he is currently expected to renew it for another term, he has shown signs of wanting to branch out beyond late night.

Perhaps the biggest challenge is the format of the new show. Comedy Central has a tradition of coming up with completely new formats that disrupt the existing state of play. When Mr. Stewart took over "The Daily Show," he reinvented it as political satire. And Mr. Colbert's conservative blowhard character is unmatched.

In launching "@midnight," last fall, Comedy Central debuted another format that is new to late night: an interactive talk show disguised as a game show. The show ranks fourth in audience in the 18-34 age category behind "The Tonight Show" and its two fellow Comedy Central late-night shows.

Comedy Central isn't ruling out another character-led show, albeit a very different one from Mr. Colbert's. "It could be a person playing a character but it could also be a new format we haven't thought of yet," said Ms. Ganeless. "The challenge begins."

Write to Merissa Marr at merissa.marr@wsj.com

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