There's a season 12 press release which mentions several characters who debuted in season 12, but I'm starting to wonder if any of them actually did debut that season. Most of them seem to have debuted before.
Assuming 40 Years of Sunny Days is accurate, Dr. Nobel Price appeared at least once in season 11. It's possible he was meant to be a one-shot character who got promoted to recurring character status the next year, or maybe they did do multiple News Flash segments with him in season 11 and then in season 12 started having him featured in street scenes.
Telly first appeared, in an alternate form, in season 10, then became the Telly we all know in season 11, though it might have been season 12 when he became a main character.
Muppet Wiki says that Forgetful Jones first appeared in 1979, but I wonder if there's a source for that (did Michael Earl say it somewhere?). I haven't seen any official evidence that Forgetful first appeared in season 11. Ditto for Clementine. The Buster puppet had been around as early as season 5 but wouldn't be known as Buster until season 12 (I assume).
Elmo first appeared in season 11, but was a generic monster. He's first known to have been known as Elmo in season 12, but with him gaining a name and something of a character hook (talking in sounds, apparently... even if the season did repeat the previous seasons sketches where he talked properly), I'll accept that as his proper debut season.
All this time, I thought Deena and Pearl debuted in season 12, but I've seen a number of season 11 episode summaries that mention the two (especially Deena, but I did see one episode summary listing a Deena and Pearl sketch). I guess that means Karen Prell was there for two seasons (I do recall an article/interview with her, from around 2005, which said that she performed on Sesame Street from 1979-1980, when other sources say it was 1980-1981).
Poco Loco was around as early as season 6, with his name, not sure how major he was back then, but it seems they treated him like a more major character in season 12.
Currently, there's no evidence that Countess von Dahling, Masha, the Honkers, or Ferlinghetti Donnizetti debuted before season 12.