On Broadway, at least, everyone loves a pompous, thin-skinned autocrat. It’s why Taran Killam couldn’t be more excited to join “Hamilton” as King George, the blustery British monarch who, with a few memorable pop tunes, warns the upstart American colonists that they’ll regret their revolutionary acts. The role, which Mr. Killam inherits from Rory O’Malley (Jonathan Groff, Andrew Rannells and Brian d’Arcy James have also played the character), will be his Broadway debut when he begins on Jan. 17.

It’s a big opportunity for Mr. Killam, 34, an alumnus of “Saturday Night Live” who is close with the “Hamilton” creator, Lin-Manuel Miranda, and its director, Thomas Kail. “I don’t want to let my friends down, more than anything,” Mr. Killam said in late December over a pub lunch in TriBeCa.

This is also the first major project that Mr. Killam will be seen in since it was reported last summer that he would not be returning to “S.N.L.,” where he had spent six seasons playing politicians like Donald J. Trump, Ted Cruz and Paul D. Ryan, as well as characters like Jebidiah Atkinson, a feisty newspaper critic from the 1860s.

Mr. Killam had recently returned to NBC’s Manhattan headquarters to appear on “Late Night With Seth Meyers.” Though “S.N.L.” was dark that week, he did not want to seem too eager to roam the sets and offices. “It’s still too fresh,” Mr. Killam said. “I didn’t want to be Matthew McConaughey from ‘Dazed and Confused.’”