Jon Bokenkamp, the creator and executive producer of “The Blacklist” is taking a few moments to catch his breath after a frantic season finale Thursday night. Season 3 was set up to be a bit of a change because the show’s main character, Liz Keen (Megan Boone), was moving from being a hunter, as an FBI agent, to being the hunted, as a suspected Russian spy.

The success of the show led NBC to ask to see what a spin-off might be like, which caused Bokenkamp to turn one of the final episodes of season 3 into a pilot for what...